Question

If A = 30° and B = 60°, verify 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