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°

= ${\displaystyle \frac{\sqrt{3}}{2}\times \frac{1}{2}-\frac{1}{2}\times \frac{\sqrt{3}}{2}}$

= ${\displaystyle \frac{\sqrt{3}}{4}-\frac{\sqrt{3}}{4}}$
= 0
L.H.S = R.H.S.
Therefore,
sin(A - B) = sinA cosB - cosA sinB.