Question

2sin11π/30-sinπ/30-cos8π/15-cos2π/15
вычислите

Answer 1

$2cdot sin frac{11pi }{30}-sinfrac{pi}{30}-cosfrac{8pi }{15}-cosfrac{2pi}{15}=\\=2cdot sinfrac{11pi}{30}-sinfrac{pi }{30}-cos(frac{pi}{2}+frac{pi}{30})-cos(frac{pi}{2}-frac{11pi}{30})=\\=2cdot sinfrac{11pi}{30}-sin frac{pi }{30} +sin frac{pi }{30} -sinfrac{11pi }{30}=sinfrac{11pi}{30}=sin66^circ =cos24^circ$