Use a doubleangle identity to find the exact value of the ex

Use a double-angle identity to find the exact value of the expression. 2 tan pi/8/1- tan^2 pi/8 Choose the correct answer below. 1/2 Squareroot 3/3 Squareroot 3 Squareroot 3/2 -Squareroot 3 1

Solution

(2 tan pi/8) / (1 - tan^2 pi/8 )

applying double angle formula

tan 2 a = 2 tan a / 1 - tan^2 a

therefore,

(2 tan pi/8) / (1 - tan^2 pi/8 ) = tan 2 ( pi/8 ) = tan pi/4

tan pi/4 = 1

option f