Question

Prove that cos(a-b) - cos(a+b) = 2sina sinb

Answer 1

We know:
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

cos(a - b) - cos(a + b) = 2sin(a)sin(b)

L = cos(a)cos(b) + sin(a)sin(b) - (cos(a)cos(b) - sin(a)sin(b))

= cos(a)cos(b) + sin(a)sin(b) - cos(a)cos(b) + sin(a)sin(b)

= 2sin(a)sin(b) = R