What is the exact value of

Question

tan(cos^−1(3/7 ))? 

Answer 1

tan(cos^{- 1} (3/7))

Let cos^{- 1} (3/7) = t, then cost = 3/7.

cos(t) = Adjacent side/ Hypotenuse = 3/7

From pythagorean theorem,

Opposite side = √(Hypotenuse² - Adjacent side² )

= √(49 - 9) = √40

tan(cos^{- 1} [3/7]) = tan(t)

tan(t) = Opposite side/ Adjacent side

tan(t) = √40/3

tan(cos^{- 1} (3/7)) = √40/3.