Question

In Problems 79-90, find the exact value of each expression.

$\cos \left(2{\sin }^{-1}\frac{3}{5}\right)$

Short answer

The exact value is$\frac{7}{25}$

Step-by-step solution

Given information

Given expression$\cos \left(2{\sin }^{-1}\frac{3}{5}\right)$

Assume θ=sin-135 and use double angle formula

Using double angle, we get

$$\begin{gathered} \cos \left(2\theta \right)=1-2{\left(\frac{3}{5}\right)}^2 \\ \cos \left(2\theta \right)=1-2·\frac{9}{25} \\ \cos \left(2\theta \right)=\frac{7}{25} \end{gathered}$$