The correct option is D 2425 Given sin(2sin^ 14/5) Let sin^ 14/5=t ⇒ sin t=4/5 ∴ sin(2 sin^ 14/5) = sin 2t = 2 sin t cos t ...

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Domain and Range of Basic Inverse Trigonometric Functions

Solve sin2s...

Question

Solve
$sin (2 {sin}^{- 1} \frac{4}{5})$

\frac{24}{29}

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\frac{34}{25}

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- \frac{24}{25}

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\frac{24}{25}

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Solution

The correct option is D $\frac{24}{25}$
Given
$s i n (2 s i n^{- 1} \frac{4}{5})$
Let $s i n^{- 1} \frac{4}{5} = t$
$\Rightarrow s i n t = \frac{4}{5}$
$∴ s i n (2 s i n^{- 1} \frac{4}{5})$
$= s i n 2 t$
$= 2 s i n t c o s t$
$= 2 \times \frac{4}{5} \times \sqrt{1 - s i n^{2} t}$
$= \frac{8}{5} \times \sqrt{1 - \frac{16}{25}}$
$= \frac{8}{5} \times \frac{3}{5} = \frac{24}{25}$
Hence, $s i n (2 s i n^{- 1} \frac{4}{5}) = \frac{24}{25}$

Suggest Corrections

$23$	$24$	$25$	$26$	$27$	$23$	$24$
$25$	$28$	$24$	$29$	$19$	$20$	$x$

Class interval	$0 - 9$	$10 - 14$	$15 - 24$	$25 - 29$	$30 - 34$
Frequency	$6$	$4$	$12$	$10$	$8$

Marks	$0 - 4$	$5 - 9$	$10 - 14$	$15 - 19$	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$
Frquency	$2$	$5$	$7$	$13$	$21$	$16$	$8$	$3$