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

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Answer 1 · 2017-02-06T16:22:36

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

The expression is

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

Use iteratively

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

for successive doubling of angles.

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