Question

What is `2sin(theta/2-pi/4)-cos(theta/2)` in terms of trigonometric functions of a unit `theta`?

Answer 1

Please look below.

Explanation:

`2sin(theta/2 - pi/4) - cos(theta/2)`
`= 2(sin(theta/2)cos(pi/4) - sin(pi/4)cos(theta/2)) - cos(theta/2)`
`= sqrt2sin(theta/2) - sqrt(2)cos(theta/2) - cos(theta/2)`
`= sqrt2sin(theta/2) - (1+ sqrt2)cos(theta/2)`