Question

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

Answer 1

`4/sqrt19`

Explanation:

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.