Question

Sin(-45градусов)tgП/3+cos(-45)ctgП/6

Answer 1

$sin( -frac{pi}{4} )*tg( frac{pi}{3} )+cos(- frac{pi}{4} )*ctg( frac{pi}{6} )=$
$=-sin(frac{pi}{4} )*tg( frac{pi}{3} )+cos(frac{pi}{4} )*ctg( frac{pi}{6} )=$
$=- frac{ sqrt{2} }{2}* frac{sin( frac{pi}{3} )}{cos( frac{pi}{3} )} + frac{ sqrt{2} }{2} * frac{cos( frac{pi}{6} )}{sin( frac{pi}{6} )} =$
$=- frac{ sqrt{2} }{2}* frac{ frac{ sqrt{3} }{2}}{ frac{1}{2}} + frac{ sqrt{2} }{2} * frac{frac{ sqrt{3} }{2}}{ frac{1}{2}} =0$