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Inverse Trigonometric Functions question

2022 · 25 Jul · Shift 2 · Q45

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JEE Main
Mathematics
Inverse Trigonometric Functions
2022 · 25 Jul · Shift 2 · Q45

Inverse Trigonometric Functions question

2022 · 25 Jul · Shift 2 · Q45

JEE MainMathematicsInverse Trigonometric FunctionsNumerical+4 / −1

Let

x = \sin (2{\tan ^{ - 1}}\alpha )

and

y = \sin \left( {{1 \over 2}{{\tan }^{ - 1}}{4 \over 3}} \right)

. If

S = \{ a \in R:{y^2} = 1 - x\}

, then

\sum\limits_{\alpha \in S}^{} {16{\alpha ^3}}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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