Please help with this trig identity?

Question

cos((3pi/2)-x)+cos((3pi/2)+x)=0

Answer 1

cos((3π/ 2) - x) + cos((3π/ 2) + x)

Recall :Trigonometry co function identities  cos((3π/ 2) - x) = -sinx and cos((3π/ 2) + x) = sinx

Substitute cos((3π/ 2) - x) = -sinx and cos((3π/ 2) + x) = sinx in the above problem

 -sinx + sinx = 0.

Hence the given problem is solved