Question

How do you prove `sin( (3π/2) + x ) + sin ( (3π/2) - x ) = - 2 cos x`?

Answer 1

Use `sin(A+B)+sin(A-B) = 2 sin A cos B`.

Explanation:

Here, A = `3pi/2` and B = x.
`sin(3pi/2) = sin (pi+pi/2)=-sin(pi/2)=-1.`