Question

find the value of 2 cos 5pi/12 cos 7pi/12​

Answer 1

Step-by-step explanation:

$2 \cos( \frac{5\pi}{12} ) \cos( \frac{7\pi}{12} ) = 2 \cos( \frac{5\pi}{12} ) \cos(\pi - \frac{5\pi}{12} )$

$2 \cos( \frac{5\pi}{12} )( - \cos( \frac{5\pi}{12} ) = - 2 \cos ^{2} ( \frac{5\pi}{12} )$

$= - (1 + \cos(2( \frac{5\pi}{12} ))$

$= - (1 + \cos( \frac{5\pi}{6} )$

$= - 1 + \frac{ \sqrt{3} }{2}$

$= \frac{ \sqrt{3} - 2}{2}$