Trigonometry-JEE-Main-PYQ’s

Mathematics Questions

If the value of $\frac{3 \cos 36^\circ + 5 \sin 18^\circ}{5 \cos 36^\circ - 3 \sin 18^\circ}$ is $\frac{a\sqrt{5} - b}{c}$ , where $a, b, c$ are natural numbers and $\gcd(a, c) = 1$ , then $a + b + c$ is equal to:

(A) 54

(B) 52

(D) 40

Click to View Answer

Correct Answer: [ ]

If $\sin x = -\frac{3}{5}$ , where $\pi < x < \frac{3\pi}{2}$ , then $80 \left( \tan^2 x - \cos x \right)$ is equal to

(A) 109

(B) 108

(D) 18

Click to View Answer

Correct Answer: [ ]

Suppose $\theta \in \left[0, \frac{\pi}{4}\right]$ is a solution of $4 \cos \theta - 3 \sin \theta = 1$ . Then $\cos \theta$ is equal to:

(A) $\frac{6 - \sqrt{6}}{3\sqrt{6} - 2}$

(B) $\frac{4}{3\sqrt{6} + 2}$

(D) $\frac{4}{3\sqrt{6} - 2}$

Click to View Answer

Correct Answer: [ ]

If $\tan A = \frac{1}{\sqrt{x(x^2 + x + 1)}}$ , $\tan B = \frac{\sqrt{x}}{\sqrt{x^2 + x + 1}}$ and
$\tan C = (x^{-3} + x^{-2} + x^{-1})^{1/2}$ , $0 < A, B, C < \frac{\pi}{2}$ , then $A + B$ is equal to:

(A) $C$

(B) $\pi - C$

(D) $\frac{\pi}{2} - C$

Click to View Answer

Correct Answer: [ ]

The number of solutions, of the equation

$e^{\sin x} - 2e^{-\sin x} = 2$ , is:

(A) 0

(B) 1

(D) more than 2

Click to View Answer

Correct Answer: [ ]

For $\alpha, \beta \in (0, \pi/2)$ , let $3 \sin(\alpha + \beta) = 2 \sin(\alpha - \beta)$ and a real number $k$ be such that $\tan \alpha = k \tan \beta$ . Then, the value of $k$ is equal to:

(A) 5

(B) $-2/3$

(D) $2/3$

Click to View Answer

Correct Answer: [ ]

Solve the equation $\cos \theta = \frac{1}{2}$ for $\theta$ in the interval $[0, 2\pi)$ . The number of solutions is:

(A) 0

(B) 1

(D) 3

Click to View Answer

Correct Answer: [ ]

The value of

$36 \left(4 \cos^2 9^\circ - 1\right) \left(4 \cos^2 27^\circ - 1\right) \left(4 \cos^2 81^\circ - 1\right) \left(4 \cos^2 243^\circ - 1\right)$ is:

(A) 18

(B) 36

(D) 27

Click to View Answer

Correct Answer: [ ]

If $\tan 15^\circ + \frac{1}{\tan 75^\circ} + \frac{1}{\tan 105^\circ} + \tan 195^\circ = 2a$ , then the value of $\left( a + \frac{1}{a} \right)$ is: