How do you find the exact value of $cos(tan^-1(sqrt3/4))$ ?

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Answer 1 · 2016-11-28T03:44:52

$4/sqrt19$

Let $a =tan^(-1)(sqrt3/4) in Q_1$ , wherein cosine is positive.

The given expression is

$cos a = 4/sqrt((sqrt3)^2+4^2)=4/sqrt19$ ,

using definitions

tan a = (opposite side)/ (adjacent side) and

cos a = (adjacent side)/hypotenuse.

How do you find the exact value of cos(tan^-1(sqrt3/4))cos(tan^-1(sqrt3/4))?