Question

Решите 4√3cos^2(23p/12)-2√3

Answer 1

$4 \sqrt{3}cos^2( \frac{23 \pi }{12}) -2 \sqrt{3}=4 \sqrt{3}cos^2(2 \pi - \frac{ \pi }{12}) -2 \sqrt{3}=\\ =4 \sqrt{3}cos^2 \frac{ \pi }{12} -2 \sqrt{3}=2 \sqrt{3}(2cos^2( \frac{\pi }{12}) -1) = 2 \sqrt{3}*cos \frac{2\pi }{12}=\\ =2 \sqrt{3}*cos \frac{\pi }{6}=2 \sqrt{3}* \frac{ \sqrt{3} }{2} = 3$