Question

prove cos(pi-x)= -cosx

Answer 1

cos (pi-x) is x degrees above the -x axis in quadrant II

Draw it and look at the triangle
cos(pi-x) = - cos x
sin(pi-x) = + sin x
or I suppose use trig
cos(A-B) = cosA cos B + sin A sin B
so
cos(pi-x) = cos pi cos x + sin pi sin x
= -1 cos x + 0 sin x