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If A=30⁰ and B=60⁰ , then verify that sin(A+B) = sin A cos B + cos A sin B​

Answer»

\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b) \\ \sin(30 + 60) = \sin(30) \cos(60) + \cos(30) \sin(60) \\ \sin(90) = { \sin}^{2} 30 + { \cos }^{2} 30 \\ 1 = { (\frac{1}{2}) }^{2} + { (\frac{ \sqrt{3} }{2} )}^{2} \\ 1 = \frac{1}{4} + \frac{3}{4} \\ 1 = 1

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