If A = and B = , verify that: sin (A + B) = sin A cos B + cos A sin B

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Solution

Q.
If A = $60^{o}$ and B = $30^{o}$ , verify that: sin (A + B) = sin A cos B + cos A sin B

Ans.
LHS = sin(A + B) = sin(60° + 30°) = sin 90° = 1

RHS = sin A cos B + cos A sin B

= sin 60° cos 30° + cos 60° sin 30°

$= \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2} = \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$

$∴$ LHS = RHS

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