Question

Prove the equation cos(a+b).cos(a-b)=cos^2a - sin^2b. Show your solution.

Answer 1

(cos(a + b))(cos(a - b)) = cos²(a) - sin²(b)
(cos(a)cos(b) - sin(a)sin(b))(cos(a)cos(b) + sin(a)sin(b)) = cos²(a) - sin²(b)
cos²(a)cos²(b) + sin(a)cos(a)sin(a)cos(b) - sin(a)cos(b)sin(a)cos(b) - sin²(a)sin²(b) = cos²(a) - sin²(b)
cos²(a)cos²(b) - sin²(a)sin²(b) = cos²(a) - sin²(b)
cos²(a + b) = cos²(a) - sin²(b)