Trigonometry Question

Question

Find the exact value of cos(x/2) if cos(x)= -1/5, and 90 degrees < x < 180 degrees

Answer 1

You get the half-angle formula from the double angle formula as follow

cos²x - sin²x = cos 2x

2 cos²x-1 = cos 2x

cos x = sqrt[(1+cos 2x)/2]

Now substitute x/2 for x and you have the half-angle formula which will enable you to solve this problem.