Упростите выражение cos^2(п-а)+cos^2(3п/2-а)

Question

Упростите выражение cos^2(п-а)+cos^2(3п/2-а)

Answer 1

Cos² (π-α) + cos² (3π/2 -α) =1

1) cos(π-α)=-cos(-α)=-cosα
2) cos(3π/2-α)= cos(π+(π/2-α))=-cos(π/2-α)=-(-sin(-α))=-sinα
3) (-cosα)² + (-sinα)²=cos²α+sin²α=1