Question

If A = 60° and B =30°, verify that sin(A -B) = sin A cos B - cos A sin B

Answer 1

Verification for this:

Just plug in the values,

Using,

LHS = sin(60°-30°) = sin30° = 0.5

Using,

RHS

sinAcosB - cosA sinB = sin60°cos30° - cos60°sin30°

$= \frac{ \sqrt{3} }{2} ( \frac{ \sqrt{3} }{2} ) - \frac{1}{2} ( \frac{1}{2} ) \\ = \frac{3}{4} - \frac{1}{4} \\ = \frac{2}{4} \\ = \frac{1}{2} \\ = 0.5$

Since LHS = RHS

Hence proved.