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°)
= cos90°
=0

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)`

= 0
LHS  = RHS