Question

If A = 30° and B = 60°, verify that: cos (A + B) = cos A cos B − sin A sin B

Given A = 60° and B = 30°, prove that: cos (A+ B) = cos A cos B − sin A sin B

Answer 1

A = 30° and B = 60°

L.H.S.

= cos(A + B)

= cos(30° + 60°)

= cos90°

= 0

R.H.S.

= cosA cosB - sinA sinB

= cos30° x cos60° - sin30° x sin60°

= `sqrt(3)/(2) xx (1)/(2) - (1)/(2) xx sqrt(3)/(2)`

= `sqrt(3)/(4) - sqrt(3)/(4)`

= 0

⇒ cos(A + B) = cosA cosB - sinA sinB