Question

How do you express `f(theta)=-5cos(theta/8)-sin(-theta/4+pi/2)` in terms of trigonometric functions of a whole theta?

Answer 1

`-(5sqrt(1/2(1+1/2sqrt(1+1/2sqrt(1+costheta))))+sqrt(1/2+1/2sqrt(1+costheta)))`

Explanation:

The expression is

`-(5cos(theta/8)+cos(theta/4))`

Use iteratively

`cos a = sqrt(1/2(1+cos2a)`,

for successive doubling of angles.