Answer
$1$
Work Step by Step
First, we solve sin$^{-1}\frac{\sqrt2}{2}$. The interval of the inverse of sine is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a value of $\frac{\sqrt2}{2}$ in that interval. The answer is $\frac{\pi}{4}$
Now, we can solve tan$\left(\frac{\pi}{4}\right)$ which is $1$
