1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

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 2021 (Online) 26th August Evening Shift
+4
-1
The value of

$$2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} \right)$$ is :
A
$${1 \over {4\sqrt 2 }}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${1 \over {8\sqrt 2 }}$$
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
If $$\tan \left( {{\pi \over 9}} \right),x,\tan \left( {{{7\pi } \over {18}}} \right)$$ are in arithmetic progression and $$\tan \left( {{\pi \over 9}} \right),y,\tan \left( {{{5\pi } \over {18}}} \right)$$ are also in arithmetic progression, then $$|x - 2y|$$ is equal to :
A
4
B
3
C
0
D
1
4
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
If $$\sin \theta + \cos \theta = {1 \over 2}$$, then 16(sin(2$$\theta$$) + cos(4$$\theta$$) + sin(6$$\theta$$)) is equal to :
A
23
B
$$-$$27
C
$$-$$23
D
27
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