Trigonometry-JEE-Main-PYQ’s

Mathematics Questions

The value of $\sin 10^\circ \cdot \sin 30^\circ \cdot \sin 50^\circ \cdot \sin 70^\circ$ is:

(A) $\frac{1}{36}$

(B) $\frac{1}{16}$

(D) $\frac{1}{18}$

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The value of $\cos^2 10^\circ - \cos 10^\circ \cos 50^\circ + \cos^2 50^\circ$ is:

(A) $\frac{3}{2} + \cos 20^\circ$

(B) $\frac{3}{4}$

(D) $\frac{3}{2}$

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If $\cos(\alpha + \beta) = \frac{3}{5}, \quad \sin(\alpha - \beta) = \frac{5}{13}, \quad \text{and} \quad 0 < \alpha, \beta < \frac{\pi}{4},$ then $\tan(2\alpha)$ is equal to:

(A) $\frac{21}{16}$

(B) $\frac{63}{52}$

(D) $\frac{63}{16}$

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The maximum value of $3\cos\theta + 5\sin \left(\theta - \frac{\pi}{6}\right)$ for any real value of $\theta$ is:

(A) $\sqrt{34}$

(B) $\sqrt{31}$

(D) $\frac{\sqrt{79}}{2}$

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The value of $\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \ldots \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is:

(A) $\frac{1}{256}$

(B) $\frac{1}{2}$

(D) $\frac{1}{512}$

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For any $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$ , the expression

$3(\cos\theta - \sin\theta)^4 + 6(\sin\theta + \cos\theta)^2 + 4\sin^6\theta$

equals:

(A) $13 - 4\cos^2\theta + 6\sin^2\theta\cos^2\theta$