Question

Решите пожалуйста cos 13n/12-cos 5n/12

Answer 1

$Cos\frac{13\pi }{12}-Cos\frac{5\pi }{12}=-2Sin\frac{\frac{13\pi }{12}+\frac{5\pi }{12}}{2}Sin\frac{\frac{13\pi }{12}-\frac{5\pi }{12}}{2}=-2Sin\frac{18\pi }{24}Sin\frac{8\pi }{24}=-2Sin\frac{3\pi}{4}Sin\frac{\pi }{3}=-2Sin(\pi-\frac{\pi }{4})Sin\frac{\pi }{3}=-2Sin\frac{\pi }{4}Sin\frac{\pi }{3}=-2*\frac{\sqrt{2} }{2}*\frac{\sqrt{3}}{2}=-\frac{\sqrt{6}}{2}$