Question
Prove that: $2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}=\frac{1}{2}$

Answer

$\text{LHS}=2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}$ $\because\ 2\cos\text{A}\cos\text{B}=\cos(\text{A+B})+\cos(\text{A}-\text{B})$ $=\ \cos\Big(\frac{5\pi}{12}+\frac{\pi}{12}\Big)+\cos\Big(\frac{5\pi}{12}-\frac{\pi}{12}\Big)$ $=\ \cos\Big(\frac{\pi}{2}\Big)+\cos\Big(\frac{\pi}{3}\Big)$ $=\ 0+\frac{1}{2}=\frac{1}{2}=\text{RHS}$

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