Question

prove that cos(45°-A).cos (45°-B)-sin(45°-A).sin(45-B)​=sin(A+B)

Answer 1

L.H.S = cos(45° – A) · cos(45° – B) – sin(45° – A) · sin(45° – B) = cos(45° – A + 45° – B) ∵ cosA . cosB – sinA . sinB = cos(90° – (A + B)) = cos (A + B) = sin(A + B) = R.H.S.