Prove that: 2 5 12 12 =1 2 - Vidyadip

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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