Question

sin2a-2sin4a*cosa +sin6a

Answer 1

$sin2 alpha +sin6 alpha =2sinfrac{2 alpha +6 alpha }{2}cdot cosfrac{6 alpha -2 alpha }{2}=2sin4 alpha cdot cos2 alpha \\\sin2 alpha -2sin4 alpha cdot cos alpha +sin6 alpha =2sin4 alpha cdot cos2 alpha -2sin4 alpha cdot cos alpha =\\=2sin4 alpha (cos2 alpha -cos alpha )=2sin4 alpha cdot (-2sinfrac{2 alpha + alpha }{2}cdot sinfrac{2 alpha - alpha }{2})=\\=-4sin4 alpha cdot sinfrac{3 alpha }{2}cdot sinfrac{ alpha }{2}$