Question

If A = B = 60°, verify that: sin(A - B) = sinA cosB - cosA sinB

Answer 1

sin(A - B) = sinA cosB - cosA sinB
L.H.S. :
sin(A - B) = sin(60°- 60°) = sin0° = 0
R.H.S. :
sinA cosB - cosA sinB
= sin60° cos60° - cos60° sin60°

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

= `sqrt(3)/(4) - sqrt(3)/(4)`
= 0
L.H.S = R.H.S.
Therefore,
sin(A - B) = sinA cosB - cosA sinB.