Express the following as the product of sines and cosines: 12x+ 4… - Vidyadip

Question

Express the following as the product of sines and cosines: $\sin12\text{x}+\sin4\text{x}$

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Answer

$\sin12\text{x}+\sin4\text{x}$ $\Big[\because\ \sin\text{C}+\sin\text{D}=2\sin\frac{\text{C+D}}{2}\cos\frac{\text{C}-\text{D}}{2}\Big]$ $=\ 2\sin\Big(\frac{12\text{x}+4\text{x}}{2}\Big)\cos\Big(\frac{12\text{x}-4\text{x}}{2}\Big)$ $=\ 2\sin8\text{x}\cos4\text{x}$

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