Question

Find the exact value of each expression.

$\tan \left({\cos }^{-1}\frac{4}{5}+{\sin }^{-1}1\right)$

Short answer

The value of the expression is$-\frac{4}{3}$

Step-by-step solution

Step 1. Given information

The given expression is$\tan \left({\cos }^{-1}\frac{4}{5}+{\sin }^{-1}1\right)$

Step 2. Solve the expression

$$\begin{gathered} \tan \left({\cos }^{-1}\frac{4}{5}+{\sin }^{-1}1\right) \\ =\tan \left(37°+90°\right) \\ =-\cot \left(37°\right) \\ =-\frac{4}{3} \end{gathered}$$