Question

prove that sin(pi-x)+cos(pi-x)=sinx-cosx

Answer 1

use the difference of 2 angles

sin(pi)cos(x) - cos(pi)sin(x) + cos(pi)cos(x) - sin(pi)sin(x)

sin(pi) = 0 and cos(pi) = -1

so you have

\[0 \times \cos(x) - (-1) \times \sin(x) + (-1)\times \cos(x) - 0 \times \sin(x)\]

I'll let you finish it

Answer 2

Thank you so much.