Chapter 8 Introduction to Trigonometry Bits for 10th Class AP Board
Multiple Choice Questions (MCQs)
Question 1.
If sec θ + tan θ = a then tan θ =
A) \(\frac{\mathrm{a}^2-1}{2 \mathrm{a}}\)
B) \(\frac{\mathrm{a}^2+1}{2 \mathrm{a}}\)
C) \(\frac{2 \mathrm{a}}{\mathrm{a}^2+1}\)
D) \(\frac{2 \mathrm{a}}{\mathrm{a}^2-1}\)
Answer:
A) \(\frac{\mathrm{a}^2-1}{2 \mathrm{a}}\)
Question 2.
tan4A + tan2A = ……………… .
A) sec4A + sec2A
B) sec4A – sec2A
C) sec2A – sec A
D) sec2A + sec A
Answer:
B) sec4A – sec2A
Question 3.
\(\frac{\sin \theta}{1+\cos \theta}\) = ………………… .
A) \(\frac{1+\cos \theta}{\sin \theta}\)
B) \(\frac{1+\sin \theta}{\cos \theta}\)
C) \(\frac{1-\cos \theta}{\sin \theta}\)
D) \(\frac{1-\sin \theta}{\cos \theta}\)
Answer:
C) \(\frac{1-\cos \theta}{\sin \theta}\)
Question 4.
\(\frac{\boldsymbol{{ sin }} \theta}{1-\cot \theta}\) + \(\frac{\boldsymbol{{ sin }} \theta}{1-\cot \theta}\) = ……………….. .
A) sin θ + cos θ
B) sec θ + tan θ
C) sec θ – tan θ
D) sin θ + cos θ
Answer:
D) sin θ + cos θ
Question 5.
2 (cos6θ + sin6θ) – 3 (sin4θ + cos4θ) = ……………….. .
A) 1
B) 0
C) 2
D) -1
Answer:
D) -1
Question 6.
If cos2θ + cos4θ = 1 then sin θ + sin6θ = …………….. .
A) 0
B) 1
C) -1
D) \(\frac{1}{2}\)
Answer:
B) 1
Question 7.
If cos A + cos2A = 1 then sin4A + sin2A = ……………….. .
A) 1
B) -1
C) 0
D) 2
Answer:
A) 1
Question 8.
(sec A + tan A) (1 – sin A) = ……………… .
A) sin A
B) cos A
C) tan A
D) cosec A
Answer:
B) cos A
Question 9.
\(\frac{1+\tan ^2 A}{1+\cot ^2 A}\) = ……………….. .
A) sin2 A
B) cos2 A
C) tan2 A
D) cot2 A
Answer:
C) tan2 A
Question 10.
If cos A = \(\frac{7}{25}\) then tan A + cot A = ……………….. .
A) \(\frac{168}{625}\)
B) \(\frac{625}{168}\)
C) \(\frac{125}{148}\)
D) \(\frac{148}{125}\)
Answer:
B) \(\frac{625}{168}\)
Question 11.
If sec2θ (1 + sin θ) (1 – sin θ) = k then K = …………….. .
A) 1
B) 0
C) -1
D) \(\frac{1}{2}\)
Answer:
A) 1
Question 12.
If cos A = \(\frac{3}{5}\) then 9 cot2A – 1 = ………………… .
A) \(\frac{16}{65}\)
B) \(\frac{65}{16}\)
C) \(\frac{7}{25}\)
D) \(\frac{25}{8}\)
Answer:
C) \(\frac{7}{25}\)
Question 13.
If cosec A + cot A = \(\frac{11}{2}\) then tan A = ……………….. .
A) \(\frac{44}{117}\)
B) \(\frac{24}{117}\)
C) \(\frac{11}{117}\)
D) \(\frac{34}{117}\)
Answer:
A) \(\frac{44}{117}\)
Question 14.
cos 1°- cos 2°.cos 3° …………….. cos 179° = ……………. .
A) 1
B) 0
C) -1
D) \(\frac{1}{2}\)
Answer:
B) 0
Question 15.
If b tan θ = a then \(\frac{a \sin \theta-b \cos \theta}{a \sin \theta+b \cos \theta}\) = ……………. .
A) \(\frac{a^2-b^2}{a^2+b^2}\)
B) \(\frac{a^2+b^2}{a^2-b^2}\)
C) \(\frac{a-b}{a+b}\)
D) \(\frac{a+b}{a-b}\)
Answer:
A) \(\frac{a^2-b^2}{a^2+b^2}\)
Question 16.
cos4θ – sin4θ = ……………… .
A) 2 sin2θ – 1
B) 2 sec2θ – 1
C) 2 cos2θ – 1
D) 2 cot2θ – 1
Answer:
C) 2 cos2θ – 1
Question 17.
If cosecθ – cotθ = \(\frac{1}{3}\) (θ ≠ 0), then the value of cos2θ – sin2θ =
A) \(\frac{7}{25}\)
B) \(\frac{9}{25}\)
C) \(\frac{8}{25}\)
D) \(\frac{6}{25}\)
Answer:
A) \(\frac{7}{25}\)
Question 18.
\(\frac{\sin \theta-2 \sin ^3 \theta}{2 \cos ^3 \theta-\cos \theta}\) = ……………. .
A) cos θ
B) sin θ
C) cot θ
D) tan θ
Answer:
D) tan θ
Question 19.
If \(\frac{\cos \theta}{1-\sin \theta}\) + \(\frac{\cos \theta}{1+\sin \theta}\) = 4, then θ = ………………. .
A) 30°
B) 60°
C) 45°
D) 90°
Answer:
B) 60°
Question 20.
\(\frac{1-\tan ^2 45^{\circ}}{1+\tan ^2 45^{\circ}}\) = ……………. .
A) 1
B) -1
C) 0
D) \(\frac{1}{\sqrt{2}}\)
Answer:
C) 0
Question 21.
5 tan2θ – 5 sec2θ = ………………… .
A) 5
B) 0
C) 10
D) -5
Answer:
D) -5
Question 22.
(1 – tan θ + sec θ) (1 + cot θ – cosec θ) = ……………….. .
A) 0
B) 1
C) 2
D) None of these
Answer:
C) 2
Question 23.
The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) = ………………… .
A) 0
B) 1
C) 2
D) \(\frac{1}{2}\)
Answer:
A) 0
Question 24.
If cos θ = \(\frac{\sqrt{b^2-a^2}}{b}\), then sin θ = ………………… .
A) \(\frac{b}{\sqrt{b^2-a^2}}\)
B) \(\frac{a}{\sqrt{b^2-a^2}}\)
C) \(\frac{b}{a}\)
D) \(\frac{a}{b}\)
Answer:
D) \(\frac{a}{b}\)
Question 25.
If sin (A + B) = \(\frac{\sqrt{3}}{2}\) sin B = \(\frac{1}{2}\), then A = ……………… .
A) 30°
B) 60°
C) 45°
D) 90°
Answer:
A) 30°
Question 26.
If cos A = \(\frac{5}{13}\), then the value of \(\frac{\sin A-\cot A}{2 \cot A}\) = ………………… .
A) \(\frac{395}{3744}\)
B) \(\frac{395}{3644}\)
C) \(\frac{295}{3859}\)
D) \(\frac{295}{2859}\)
Answer:
A) \(\frac{395}{3744}\)
Question 27.
If sin θ = \(\frac{a^2-b^2}{a^2+b^2}\) then tan θ = ………………….. .
A) \(\frac{a^2+b^2}{2 a b}\)
B) \(\frac{a^2-b^2}{2 a b}\)
C) \(\frac{a^2+b^2}{a^2-b^2}\)
D) \(\frac{2 a b}{a^2+b^2}\)
Answer:
B) \(\frac{a^2-b^2}{2 a b}\)
Question 28.
If sin (x – y) = – \(\frac{1}{2}\) and cos (x + y) = \(\frac{1}{2}\), then x = …………………. .
A) 0°
B) 30°
C) 45°
D) 60°
Answer:
C) 45°
Question 29.
If x + y = 90° and sin x: sin y = √3 : 1, then x : y = ……………….. .
A) 1 : 2
B) 1 : 3
C) 3 : 1
D) 2 : 1
Answer:
D) 2 : 1
Question 30.
If cot θ = \(\frac{2 a b}{a^2-b^2}\), then cos θ = ………………. .
A) \(\frac{a^2-b^2}{2 a b}\)
B) \(\frac{2 a b}{a^2+b^2}\)
C) \(\frac{a^2+b^2}{2 a b}\)
D) \(\frac{2 a b}{a^2-b^2}\)
Answer:
B) \(\frac{2 a b}{a^2+b^2}\)
Question 31.
Which of the following is true for all values of θ(0° ≤ θ ≤ 90°) ?
A) cos2θ – sin2θ = 1
B) cosec2θ – sec2θ = 1
C) sec2θ – tan2θ = 1
D) cot2θ – tan2θ = 1
Answer:
C) sec2θ – tan2θ = 1
Question 32.
If sinθ = \(\frac{a}{b}\), (0 ≤ θ ≤ 90°) then secθ is equal to
A) \(\frac{a}{\sqrt{b^2-a^2}}\)
B) \(\frac{b}{\sqrt{b^2-a^2}}\)
C) \(\frac{\sqrt{b^2-a^2}}{b}\)
D) \(\frac{\sqrt{b^2-a^2}}{a}\)
Answer:
B) \(\frac{b}{\sqrt{b^2-a^2}}\)
Question 33.
Which of the following is not defined?
A) sec 0°
B) cosec 90°
C) tan 90°
D) cot 90°
Answer:
C) tan 90°
Question 34.
\(\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}\) can be simplified to get
A) 2cos2
B) \(\frac{1}{2}\)sec2
C) \(\frac{2}{\sin ^2 \theta}\)
D) 2sec2
Answer:
D) 2sec2
Question 35.
\(\frac{\cos ^2 \theta}{\sin ^2 \theta}-\frac{1}{\sin ^2 \theta}\), in simplified from, is :
A) tan2θ
B) sec2θ
C) 1
D) -1
Answer:
B) sec2θ
Question 36.
Assertion (A) : For 0 < θ < 90°, cosecθ – cot θ and cosec θ + cot θ are reciprocal of each other.
Reason (R) : cot2θ – cosec2θ = 1.
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
C) A is true, R is false.
Question 37.
(secθ + tanθ) = x, (secθ – tanθ) = y then ………………. .
A) xy = 1
B) \(\frac{\mathrm{x}}{\mathrm{y}}\) = 2
C) x2 = y
D) x = \(\frac{\mathrm{y}}{\mathrm{2}}\)
Answer:
A) xy = 1
Question 38.
Identify the correct identity from the following.
A) sin2Φ – cos2Φ = 1
B) sec2θ = tan2θ – \(\frac{1}{2}\)
C) cosecθ = 1 + cot2θ
D) sec2θ – tan2θ = 1
Answer:
D) sec2θ – tan2θ = 1
Question 39.
\(\sqrt{\left(1-\cos ^2 \theta\right) \sec ^2 \theta}\) = ………………….. .
A) -sinθ
B) -cosθ
C) cotθ
D) tanθ
Answer:
D) tanθ
Question 40.
sinθ = …………….. .
A) ±\(\frac{1}{\sqrt{1+\cot ^2 \theta}}\)
B) ±\(\frac{1}{\sqrt{1-\cot ^2 \theta}}\)
C) ±\(\sqrt{1+\cot ^2 \theta}\)
D) ±\(\sqrt{1+\sec ^2 \theta}\)
Answer:
A) ±\(\frac{1}{\sqrt{1+\cot ^2 \theta}}\)
Question 41.
sinθ = …………….. .
A) ±\(\frac{\tan \theta}{\sqrt{1-\sec ^2 \theta}}\)
B) ±\(\frac{\tan \theta}{\sqrt{1+\tan ^2 \theta}}\)
C) ±\(\frac{\cos \theta}{\sqrt{1+\cot ^2 \theta}}\)
D) None
Answer:
B) ±\(\frac{\tan \theta}{\sqrt{1+\tan ^2 \theta}}\)
Question 42.
cotθ = ………………. .
A) ±\(\sqrt{1+\tan ^2 \theta}\)
B) \(\frac{ \pm \sqrt{1+\cos ^2 \theta}}{\sin \theta}\)
C) \(\frac{ \pm 1}{\sqrt{\sec ^2 \theta-1}}\)
D) \(\frac{ \pm \sqrt{1-\sin ^2 \theta}}{\sin \theta}\)
Answer:
D) \(\frac{ \pm \sqrt{1-\sin ^2 \theta}}{\sin \theta}\)
Question 43.
sec θ = ……………… .
A) \(\frac{ \pm \sqrt{1+\tan ^2 \theta}}{\tan \theta}\)
B) \(\frac{\cos \theta}{\sqrt{1-\sec ^2 \theta}}\)
C) \(\frac{1}{\sec ^2 \theta}\)
D) ±\(\frac{\sqrt{1-\cos ^2 \theta}}{\cot \theta}\)
Answer:
D) ±\(\frac{\sqrt{1-\cos ^2 \theta}}{\cot \theta}\)
Question 44.
cosecθ = ……..
A) \(\frac{\sin \theta}{\sqrt{1-\cos ^2 \theta}}\)
B) \(\sqrt{1-\cos ^2 \theta}\)
C) \(\frac{1}{\sqrt{1-\sec ^2 \theta}}\)
D) ±\(\frac{1}{\sqrt{1-\cos ^2 \theta}}\)
Answer:
D) ±\(\frac{1}{\sqrt{1-\cos ^2 \theta}}\)
Question 45.
tanθ = ……………. .
A) ±\(\frac{1}{\sqrt{{cosec}^2 \theta-1}}\)
B) ±\(\frac{1}{\cot ^2 \theta}\)
C) ±\(\sqrt{{cosec}^2 \theta+1}\)
D) None
Answer:
A) ±\(\frac{1}{\sqrt{{cosec}^2 \theta-1}}\)
Question 46.
cosθ = …………… .
A) ±\(\frac{1}{\sqrt{1+\tan ^2 \theta}}\)
B) ±\(\sqrt{1+\tan ^2 \theta}\)
C) \(\frac{1}{\cot ^2 \theta}\)
D) \(\frac{\sqrt{1+\cot ^2 \theta}}{\cot \theta}\)
Answer:
A) ±\(\frac{1}{\sqrt{1+\tan ^2 \theta}}\)
Question 47.
\(\frac{1+\tan ^2 A}{1+\cot ^2 A}\) = ……………… .
A) 1 – cot2A
B) \(\frac{\cot \mathrm{A}}{2}\)
C) cot2A
D) tan2A
Answer:
D) tan2A
Question 48.
\(\frac{1}{\sec \theta-\tan \theta}\) = …………….. .
A) secθ – tanθ
B) secθ + tanθ
C) tanθ
D) none
Answer:
B) secθ + tanθ
Question 49.
Assertion (A) : In ΔABC, ∠B = 90° then ∠A + ∠B = 100°
Reason (R) : sin2θ + cos2θ = 1
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct
C) A is true, R is false.
D) A is false, R is true.
D) A is false, R is true.
Answer:
D) A is false, R is true.
Question 50.
Assertion (A): tanθ = \(\frac{a}{b}\) then sinθ = \(\frac{b^2}{a^2}\)
Reason (R) : cosec2θ = 1 + cot2θ
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
D) A is false, R is true.
Question 51.
Assertion (A) : cosecθ – cotθ and cosecθ + cotθ are reciprocals to each other for θ < 90°
Reason (R) : cosec2θ – cot2θ = 1.
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
Question 52.
Assertion (A) : In a Right triangle ABC, ∠C = 90° then ∠A + ∠B = 90°
Reason (R) : If cosθ = sinθ, then θ = 45°
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
Question 53.
Assertion (A) : sinθ – cosθ = 0, θ ∈ Q, then θ = 45°.
Reason (R) : cosec2θ – cot2θ = 1.
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
Question 54.
Assertion (A): x . sin 30° = cos 30° then x = 1.
Reason (R) : sin 90° = 1.
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
C) A is true, R is false.
Question 55.
Assertion (A) : sin0 value increases from 0 to 90°
Reason (R): If sinθ = cosθ, then θ = 30°
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
D) A is false, R is true.
Question 56.
Assertion (A) : √2sinθ = 1 then θ = 30°
Reason (R) : tanθ is not defined if θ = 90°
A) Assertion (A) is true, Reason (R) is true and R is the correct explanation of A.
B) Assertion (A) is true, Reason (R) is true but R is not the correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
Answer:
D) A is false, R is true.
Question 57.
Match the following.
| a) \(\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}\) | i) cosec A + cot A |
| b) \(\frac{\cos \mathrm{A}-\sin \mathrm{A}+1}{\cos \mathrm{A}+\sin \mathrm{A}-1}\) | ii) 2sec A |
| c) \(\sqrt{\frac{1+\sin A}{1-\sin A}}\) | ii) sec A + tan A |
| d) \(\frac{\sin ^2 A}{1-\cos A}\) | iv \(\frac{1+\sec A}{\sec A}\) |
A) a – ii, b – i, c – iii, d – iv
B) a – i, b – ii, c – iv, d – iii
C) a – iv, b – i, c – iii, d – ii
D) a – iii, b – iv, c – ii, d – i
Answer:
A) a – ii, b – i, c – iii, d – iv
| a) \(\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}\) | ii) 2sec A |
| b) \(\frac{\cos \mathrm{A}-\sin \mathrm{A}+1}{\cos \mathrm{A}+\sin \mathrm{A}-1}\) | i) cosec A + cot A |
| c) \(\sqrt{\frac{1+\sin A}{1-\sin A}}\) | iii) sec A + tan A |
| d) \(\frac{\sin ^2 A}{1-\cos A}\) | iv \(\frac{1+\sec A}{\sec A}\) |
Question 58.
Which of the following is not true ?
A) sin (90° – θ) = cosec θ
B) sin2θ + cos2θ = 1
C) cosec θ. sin θ = 1
D) Sin 90° = 1
Answer:
A) sin (90° – θ) = cosec θ
Question 59.
Match the following :
| a) tan θ = | i) \(\frac{\cos \theta}{\sin \theta}\) |
| b) cot θ = | ii) \(\sqrt{1+\cot ^2 \theta}\) |
| c) cosec θ = | iii) \(\sqrt{\sec ^2 \theta-1}\) |
A) a → (i), b → (ii), c → (iii)
B) a → (ii), b → (iii), c → (i)
C) a → (iii), b → (i), c → (ii)
D) a → (ii), b → (i), c → (iii)
Answer:
C) a → (iii), b → (i), c → (ii)
| a) tan θ = | iii) \(\sqrt{\sec ^2 \theta-1}\) |
| b) cot θ = | i) \(\frac{\cos \theta}{\sin \theta}\) |
| c) cosec θ = | ii) \(\sqrt{1+\cot ^2 \theta}\) |
Question 60.
Match the following :
| p) \(\frac{\sqrt{1-\cos ^2 \theta}}{\cos \theta}\) | i) sec θ |
| q) tan θ cosec θ cot θ | ii) cosec θ |
| r) cosec (90° – θ) | iii) tan θ |
A) p → (i), q → (iii), r → (ii)
B) p → (iii), q → (ii), r → (i)
C) p → (ii), q → (i), r → (iii)
D) p → (iii), q → (i), r → (ii)
Answer:
B) p → (iii), q → (ii), r → (i)
| p) \(\frac{\sqrt{1-\cos ^2 \theta}}{\cos \theta}\) | iii) tan θ |
| q) tan θ cosec θ cot θ | ii) cosec θ |
| r) cosec (90° – θ) | i) sec θ |
Question 61.
Match the following :
| P) sin θ | i) \(\frac{1}{\sec \theta}\) |
| Q) cos θ | ii) \(\sqrt{\sec ^2 \theta-1}\) |
| R) tan θ | iii) \(\sqrt{\frac{\sec ^2 \theta-1}{\sec ^2 \theta}}\) |
Choose the correct answer.
A) P → (i), Q → (ii), R → (iii)
B) P → (iii), Q → (i), R → (ii)
C) P → (iii), Q →(ii), R → (i)
D) P → (i), Q → (iii), R → (ii)
Answer:
B) P → (iii), Q → (i), R → (ii)
| P) sin θ | iii) \(\sqrt{\frac{\sec ^2 \theta-1}{\sec ^2 \theta}}\) |
| Q) cos θ | i) \(\frac{1}{\sec \theta}\) |
| R) tan θ | ii) \(\sqrt{\sec ^2 \theta-1}\) |
Question 62.
If sin θ = \(\frac{3}{5}\), then the value of cos θ is (θ is acute angle) ………………… .
A) \(\frac{1}{5}\)
B) \(\frac{5}{3}\)
C) \(\frac{4}{5}\)
D) \(\frac{2}{5}\)
Answer:
C) \(\frac{4}{5}\)
Question 63.
If θ is acute angle, then sin θ × sec θ = ……………… .
A) tan θ
B) cot θ
C) 1
D) cosec θ
Answer:
A) tan θ
Question 64.
If Δ ABC is right-angled at C, then the value of cos (A + B) is ……………….. .
A) 0
B) \(\frac{1}{2}\)
C) \(\frac{\sqrt{3}}{2}\)
D) 1
Answer:
A) 0
Question 65.
The value of (sin 30° + cos 60°) – (sin 60° + cos 30°) is ……………… .
A) 0
B) 1 + 2√3
C) 1 – √3
D) 1 + √3
Answer:
C) 1 – √3
Question 66.
In ΔABC, ∠B = 90, then cos(A + C) = ?
A) 1
B) 0
C) \(\frac{1}{2}\)
D) \(\frac{\sqrt{3}}{2}\)
Answer:
D) \(\frac{\sqrt{3}}{2}\)
Fill in the blanks:
1. If sin θ + cos θ = √3, then tan θ + cot θ = _________ .
Answer:
1
2. If sec θ + tan θ = \(\frac{1}{a}\), then sec θ – tan θ = _________ .
Answer:
a
3. If 1 – sin2θ = 3 sin θ cos θ, then tan θ = _________ .
Answer:
\(\frac{1}{3}\)
4. cot θ in terms of cos θ is _________ .
Answer:
\(\frac{\cos \theta}{\sqrt{1-\cos ^2 \theta}}\)
5. The value of (1 + cot2θ) (1 – cos θ) (1 + cos θ) is _________ .
Answer:
1
6. If sin (A + B) = \(\frac{1}{2}\) and cos (A – B) = \(\frac{1}{2}\), then cosec A = _________ .
Answer:
√2
7. If x + y = 90° and y = 2x, then tan x-tan y ________ .
Answer:
1
8. If tan A = \(\frac{4}{3}\), then sin A = _________ .
Answer:
\(\frac{4}{5}\)
9. sin 60°-cos 30° + sin 30°-cos 60° = ________ .
Answer:
1
10. If 15 cot A = 8, then cosec A = _________ .
Answer:
\(\frac{17}{15}\)
11. If 3a = sec θ and \(\frac{3}{a}\) = tan θ, then 3(a2 – \(\frac{1}{a^2}\) = ________ .
Answer:
\(\frac{1}{3}\)
12. If cosec θ = 5a and cot θ = \(\frac{5}{a}\), then the value of 5(a2 – \(\frac{1}{a^2}\) = _________ .
Answer:
\(\frac{1}{5}\)
13. If x = a sin θ and y = b cos θ, then b2x2 + a2y2 = _________ .
Answer:
a2.b2
14. sin2θ + \(\frac{1}{1+\tan ^2 \theta}\) = _________ .
Answer:
1
15. (1 + cot2θ) sin2θ = _________ .
Answer:
1