Question

Вычислите: (sin5α-sinα)/(sin5αcos3α-cos5αsin3α) 

Answer 1

$\dfrac{\sin5\alpha -\sin\alpha }{\sin5\alpha \cos3\alpha -\cos5\alpha \sin3\alpha }=\dfrac{2\sin\frac{5\alpha-\alpha }{2} \cos\frac{5\alpha+\alpha }{2} }{\sin(5\alpha-3\alpha) }=\dfrac{2\sin2\alpha \cos3\alpha }{\sin2\alpha }=2\cos3\alpha$