Question

If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B

Answer 1

Given that A = B = 45°

LHS = sin (A – B)

= sin ( 45° – 45°)

= sin 0°

= 0

RHS = sin A cos B – cos A sin B

= sin 45° cos 45° – cos 45° sin 45°

= `(1)/(sqrt2) (1)/(sqrt2) – (1)/(sqrt2) (1)/(sqrt2)`

= 0

LHS = RHS