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

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Answer 1 · 2016-08-23T16:27:34

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

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,

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

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