Find the exact value of $\tan\left ( \sin^{-1} \left ( \sqrt 2/2 \right )\right )$ 
Find the exact value of $\tan\left ( \sin^{-1} \left ( \dfrac{\sqrt{2}}{2} \right )\right )$ without using a calculator. 

I started by finding $\sin^{-1} \left ( \dfrac{\sqrt{2}}{2} \right )=\dfrac{\pi}{4}$
So, $\tan\left ( \sin^{-1} \left ( \dfrac{\sqrt{2}}{2} \right )\right )=\tan\left( \dfrac{\pi}{4}\right)$. 
The answer is $1$. Can you show how to solve $\tan\left( \dfrac{\pi}{4}\right)$ to get $1$? Thank you. 

We have to find the exact value of $\;\tan\left(\sin^{-1}\dfrac{1}{\sqrt{2}}\right)$.
Since $\;\sin(45)=\dfrac{1}{\sqrt{2}}\;,\;x=45\;$ so $\;\tan(45)=1\;,\;$ hence we are done.  Now $\;\sin(45)=\cos(45)\;,\;$ thus $\;\tan(45)=1\;.$
