Write as a single trig function value using half angle or do

Write as a single trig function value using half angle or double angle formulas. squareroot 1 - cos(-2 pi/7)/2 = sin (-pi/7) -cos pi/7 sin (pi/7) cos(-pi/7)

Solution

sqrt{ ( 1 -cos(-2pi/7) /2}

we know cos(-x) = cosx

use formula cos2x = 1- 2sin^2x

sqrt{ ( 1 -cos(-2pi/7) /2} = sqrt { (2sin^2(pi/7)/2 }

= sqrt{sin^2(pi/7)}

sin(pi/7)