Question

2 cos ( x – pie/2) + 3 sin (x + pie/2) - (3sin x + 2cos x )

Answer 1

use the sin(A+B) and cos(A-B) expansions

2 cos ( x – π/2) + 3 sin (x + π/2) - (3sin x + 2cos x )
= 2(cosx*coxπ/2) + sinx*sinπ/2) + 3(sinx*cosπ/2 + cosx*sinπ/2) - 3sinx - 2cosx
= 2(cosx*0 + sinx*1) + 3(sinx*0 + cosx*1) - 3sinx - 2cosx
= ....
carry on

Answer 2

first, that's pi, not pie!
Don't any teachers actually show how to spell Greek letters any more?
2 cos(x - π/2) + 3 sin(x + π/2) - (3sinx + 2cosx)
= 2sinx + 3cosx - 3sinx - 2cosx
= cosx - sinx

You must be studying the sum/difference formulas for sin and cos.
Better review them some more.

Answer 3

Thank u so much sir.