Question

Solve

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

• A. $\frac{24}{29}$
• B. $\frac{34}{25}$
• C. $-\frac{24}{25}$
• D. $\frac{24}{25}$

Answer 1

The correct option is D $\frac{24}{25}$

Given

$sin\left(2si{n}^{-1}\frac{4}{5}\right)$

Let $si{n}^{-1}\frac{4}{5}=t$

$\Rightarrow sint=\frac{4}{5}$

$\therefore sin\left(2si{n}^{-1}\frac{4}{5}\right)$

$=sin2t$

$=2sintcost$

$=2\times \frac{4}{5}\times \sqrt{1-si{n}^{2}t}$

$=\frac{8}{5}\times \sqrt{1-\frac{16}{25}}$

$=\frac{8}{5}\times \frac{3}{5}=\frac{24}{25}$

Hence, $sin\left(2si{n}^{-1}\frac{4}{5}\right)=\frac{24}{25}$