Question

1) sin 7pi\3 * cos 2pi\3 * tg 9pi\4 *ctg 13pi\6 * cos 7pi\4 2) sin 5pi\3 * cos 7pi\6 * tg 11pi\4 * ctg 8pi\3 * cos 11pi\6

Answer 1

$1)=sin(2 \pi + \frac{ \pi }{3} )*cos( \pi - \frac{ \pi }{3})*tg(2 \pi + \frac{ \pi }{4} )*ctg(2 \pi + \frac{ \pi }{6})*cos(2 \pi - \frac{ \pi }{4})$
$=sin \frac{ \pi }{3}*(-cos \frac{ \pi }{3} )*tg \frac{ \pi }{4}*ctg \frac{ \pi }{6} *cos \frac{ \pi }{4}=$
$- \frac{ \sqrt{3} }{2}* \frac{1}{2}*1* \sqrt{3}* \frac{ \sqrt{2} }{2}=- \frac{3 \sqrt{2} }{8}$
$2)=sin(2 \pi - \frac{ \pi }{3})*cos( \pi + \frac{ \pi }{6})*tg(3 \pi - \frac{ \pi }{3})*ctg(3 \pi - \frac{ \pi }{3})*cos(2 \pi - \frac{ \pi }{6})$
$=(-sin \frac{ \pi }{6})*(-cos \frac{ \pi }{6})*tg(- \frac{ \pi }{4})*(-ctg \frac{ \pi }{3})*cos \frac{ \pi }{6}=$
$\frac{ \sqrt{3} }{2}* \frac{ \sqrt{3} }{2}*1* \frac{ \sqrt{3} }{3}* \frac{ \sqrt{3} }{2}= \frac{ \sqrt{81} }{24}= \frac{9}{24}= \frac{3}{8}$