Question

How do you find the exact value of `tan(cos^-1(sqrt2/2))`?

Answer 1

`tan{cos^-1(sqrt2/2)}=tan(pi/4)=1`.

Explanation:

Recall the Defn. :-

`cos^-1 x=theta, |x| <=1 iff x=costheta, theta in [0,pi]`

Knowing that, `cos(pi/4)=sqrt2/2, pi/4 in [0,pi]; cos^-1(sqrt2/2)=pi/4`.

Hence,

`tan{cos^-1(sqrt2/2)}=tan(pi/4)=1`.