Question

1)sin (-49п/6)*cos51п/3+tg (-113п/4)=2)cos37п/4*sin (-89п/4)*cos^2 (13п/3)=

Answer 1

$sin(-\frac{49\pi}{6})*cos(\frac{51\pi}{3})+tg(-\frac{113\pi}{4})=\\-sin(\frac{48\pi}{6}+\frac{\pi}{6})*cos17\pi-tg(\frac{112\pi}{4}+\frac{\pi}{4})=\\-sin(8\pi+\frac{\pi}{6})*(-1)-tg(28\pi+\frac{\pi}{4})=sin\frac{\pi}{6}-tg\frac{\pi}{4}=\frac{1}{2}-1=-\frac{1}{2};$


$cos\frac{37\pi}{4}*sin(-\frac{89\pi}{4})*cos^2(\frac{13\pi}{3})=\\cos(\frac{36\pi}{4}+\frac{\pi}{4})*(-sin(\frac{88\pi}{4}+\frac{\pi}{4})*cos^2(\frac{12\pi}{3}+\frac{\pi}{3})=\\cos(9\pi+\frac{\pi}{4})*(-sin(22\pi+\frac{\pi}{4})*cos^2(4\pi+\frac{\pi}{4})=\\-cos\frac{\pi}{4}*(-sin\frac{\pi}{4})*cos^2\frac{\pi}{4}=-\frac{\sqrt2}{2}*(-\frac{\sqrt2}{2})*(\frac{\sqrt2}{2})^2=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}$