Question

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

Answer 1

Given A = 60° and B = 30°

LHS = cos(A – B)

= cos (60° – 30°)

= cos 30°

= `(sqrt3)/(2)`

RHS = cos A cos B + sin A sin B

= cos 60° cos 30° + sin 60° sin 30°

= `(1)/(2) (sqrt3)/(2) + (sqrt3)/(2) (1)/(2)`

= `(sqrt3)/(4) + (sqrt3)/(4)`

= `(sqrt3)/(2)`

LHS = RHS