JEE (Main) Mathematics - TRIGONOMETRY Multiple Choice Questions (MCQs)
JEE (Main) Mathematics - Trigonometry MCQs
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Which of the following is an identity?
- A) \( \sin^2\theta + \cos^2\theta = 1 \)
- B) \( \tan\theta = \frac{1}{\sin\theta} \)
- C) \( \cot\theta = \frac{1}{\cos\theta} \)
- D) None of the above
Answer: A) \( \sin^2\theta + \cos^2\theta = 1 \)
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If \( \sin A = \frac{3}{5} \), then \( \cos A \) is equal to:
- A) \( \frac{4}{5} \)
- B) \( \frac{3}{5} \)
- C) \( \frac{5}{3} \)
- D) \( \frac{2}{5} \)
Answer: A) \( \frac{4}{5} \)
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The value of \( \tan\left(\frac{\pi}{4} - \theta\right) \) is:
- A) \( \frac{\tan\theta - 1}{\tan\theta + 1} \)
- B) \( \frac{\tan\theta + 1}{\tan\theta - 1} \)
- C) \( \frac{1 - \tan\theta}{1 + \tan\theta} \)
- D) \( \frac{1 + \tan\theta}{1 - \tan\theta} \)
Answer: C) \( \frac{1 - \tan\theta}{1 + \tan\theta} \)
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If \( \sec\theta = 2 \), what is the value of \( \cos\theta \)?
- A) \( \frac{1}{2} \)
- B) \( \frac{1}{\sqrt{2}} \)
- C) \( \frac{1}{4} \)
- D) \( \frac{1}{3} \)
Answer: A) \( \frac{1}{2} \)
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The value of \( \sin(2\theta) \) is:
- A) \( 2\sin\theta \cos\theta \)
- B) \( \sin\theta + \cos\theta \)
- C) \( 2\cos\theta - \sin\theta \)
- D) None of the above
Answer: A) \( 2\sin\theta \cos\theta \)
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If \( \tan\theta = 1 \), then the value of \( \sin\theta \) is:
- A) \( \frac{1}{2} \)
- B) \( \frac{\sqrt{2}}{2} \)
- C) \( \frac{1}{\sqrt{2}} \)
- D) 1
Answer: B) \( \frac{\sqrt{2}}{2} \)
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The identity \( \sec^2\theta - \tan^2\theta \) is equal to:
- A) 1
- B) 0
- C) \( \sin^2\theta \)
- D) \( \cos^2\theta \)
Answer: D) \( \cos^2\theta \)
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Which of the following is the value of \( \cos 45^\circ \)?
- A) \( \frac{1}{2} \)
- B) \( \frac{\sqrt{2}}{2} \)
- C) 1
- D) \( \frac{\sqrt{3}}{2} \)
Answer: B) \( \frac{\sqrt{2}}{2} \)
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Which of the following is the formula for \( \sin(A + B) \)?
- A) \( \sin A \cos B + \cos A \sin B \)
- B) \( \sin A \sin B + \cos A \cos B \)
- C) \( \cos A \cos B - \sin A \sin B \)
- D) \( \cos A \sin B + \sin A \cos B \)
Answer: A) \( \sin A \cos B + \cos A \sin B \)
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If \( \cos\theta = \frac{1}{4} \), then \( \sin^2\theta \) is:
- A) \( \frac{15}{16} \)
- B) \( \frac{3}{4} \)
- C) \( \frac{3}{16} \)
- D) \( \frac{1}{16} \)
Answer: A) \( \frac{15}{16} \)
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The value of \( \cot\theta \) is the reciprocal of:
- A) \( \sin\theta \)
- B) \( \cos\theta \)
- C) \( \tan\theta \)
- D) None of the above
Answer: C) \( \tan\theta \)
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Which of the following is the formula for \( \cos(2A) \)?
- A) \( 1 - 2\sin^2 A \)
- B) \( 2\cos^2 A - 1 \)
- C) \( 1 - 2\cos^2 A \)
- D) Both A and B
Answer: D) Both A and B
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If \( \sec\theta = 3 \), then \( \cos\theta \) is:
- A) \( \frac{1}{3} \)
- B) \( \frac{1}{9} \)
- C) \( \frac{3}{5} \)
- D) \( \frac{1}{5} \)
Answer: A) \( \frac{1}{3} \)
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The angle \( A \) in the identity \( \sin^2 A + \cos^2 A = 1 \) is:
- A) Any real number
- B) Between 0° and 90°
- C) Between 0° and 180°
- D) Between 0° and 360°
Answer: A) Any real number
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