Question

1. cos32°+cos28°
2. sin63°-sin27°
3. cos3/4pi+sin11/12pi

Answer 1

$cos32+cos28=2cos \frac{32+28}{2}cos \frac{32-28}{2}=2cos30cos2=2 *\frac{ \sqrt{3} }{2}cos2= \\ \sqrt{3}cos2; \\ sin63-sin27=2sin \frac{63-27}{2}cos \frac{63+27}{2}=2sin18cos45=2* \frac{ \sqrt{2} }{2}sin18= \\ \sqrt{2}sin18; \\ cos \frac{3\pi}{4}+sin \frac{11\pi}{12}= sin( \frac{\pi}{2}- \frac{3\pi}{4}) +sin \frac{11\pi}{12}= \\ 2sin \frac{ \frac{\pi}{2}- \frac{3\pi}{4}+ \frac{11\pi}{12}}{2}cos \frac{ \frac{\pi}{2}- \frac{3\pi}{4}- \frac{11\pi}{12} }{2}=2sin \frac{2\pi}{3}cos \frac{7\pi}{6}=$
$=2* \frac{ \sqrt{3} }{2} *(- \frac{ \sqrt{3}}{2} )=- \frac{3}{2} =-1,5$