Question

А) sin ( π 15 ) c o s ( 4 π 15 ) + c o s ( π 15 ) s i n ( 4 π 15 )

Answer 1

$sin(\alpha +\beta )=sin\alpha *cos\beta +cos\alpha *sin\beta$

$sin\frac{\pi }{15} *cos\frac{4\pi }{15} +cos\frac{\pi }{15}*sin\frac{4\pi }{15}=sin(\frac{\pi }{15} +\frac{4\pi }{15} )=sin\frac{5\pi }{15}=sin\frac{\pi }{3} =\frac{\sqrt{3} }{2}$