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Trigonometric Ratio and Identites question

2023 · 29 Jan · Shift 1 · Q25

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JEE Main
Mathematics
Trigonometric Ratio and Identites
2023 · 29 Jan · Shift 1 · Q25

Trigonometric Ratio and Identites question

2023 · 29 Jan · Shift 1 · Q25

JEE MainMathematicsTrigonometric Ratio and IdentitesMCQ+4 / −1

Let

f(\theta ) = 3\left( {{{\sin }^4}\left( {{{3\pi } \over 2} - \theta } \right) + {{\sin }^4}(3\pi + \theta )} \right) - 2(1 - {\sin ^2}2\theta )

and

S = \left\{ {\theta \in [0,\pi ]:f'(\theta ) = - {{\sqrt 3 } \over 2}} \right\}

. If

4\beta = \sum\limits_{\theta \in S} \theta

, then

f(\beta )

is equal to

A
$\frac{9}{8}$
B
$\frac{3}{2}$
C
$\frac{5}{4}$
D
$\frac{11}{8}$

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