Question

sin^2(17pi/18)+sin^(5pi/8)+cos^2(37pi/18)+cos^2(3pi/8)=?

Answer 1

The answer is 2.

METHOD

3π/8=π-5π/8. cos(π-5π/8)=-cos(5π/8)=cos(3π/8).

sin(π-5π/8)=sin(5π/8)=sin(3π/8).

Therefore sin²(5π/8)+cos²(3π/8)=sin²(5π/8)+cos²(5π/8)=1.

Similarly, 17π/18=3π-37π/18. cos(3π-37π/18)=-cos(37π/18)=cos(17π/8)

So sin²(17π/18)+cos²(37π/18)=1

Total sum is 1+1=2.