1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of 2sin (12$$^\circ$$) $$-$$ sin (72$$^\circ$$) is :

A
$${{\sqrt 5 (1 - \sqrt 3 )} \over 4}$$
B
$${{1 - \sqrt 5 } \over 8}$$
C
$${{\sqrt 3 (1 - \sqrt 5 )} \over 2}$$
D
$${{\sqrt 3 (1 - \sqrt 5 )} \over 4}$$
2
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of solutions of the equation

$$\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \right) = {1 \over 4}{\cos ^2}2x$$, $$x \in [ - 3\pi ,3\pi ]$$ is :

A
8
B
5
C
6
D
7
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}$$.

If $$T = \sum\limits_{\theta \, \in \,S}^{} {\cos 2\theta } $$, then T + n(S) is equal to :

A
7 + $$\sqrt 3 $$
B
9
C
8 + $$\sqrt 3 $$
D
10
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
If n is the number of solutions of the equation
$$2\cos x\left( {4\sin \left( {{\pi \over 4} + x} \right)\sin \left( {{\pi \over 4} - x} \right) - 1} \right) = 1,x \in [0,\pi ]$$ and S is the sum of all these solutions, then the ordered pair (n, S) is :
A
(3, 13$$\pi$$ / 9)
B
(2, 2$$\pi$$ / 3)
C
(2, 8$$\pi$$ / 9)
D
(3, 5$$\pi$$ / 3)
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