Question

cos(a-п)*ctg(a+п/2)*sin(4п-а)/sin(7п+а)*ctg(3п/2-а)

Answer 1

Cos(a-п)*ctg(a+п/2)*sin(4п-а)/sin(7п+а)*ctg(3п/2-а)

$frac{cos( alpha - pi )*ctg( alpha + frac{ pi }{2} )*sin(4 pi - alpha )}{sin(7 pi + alpha )*ctg( frac{3 pi }{2} - alpha )} = \ \ frac{cos ( pi - alpha )*ctg( frac{ pi }{2} + alpha )*sin(- alpha )}{sin(pi + alpha )*ctg( frac{3 pi }{2} - alpha )} = \ \ frac{-cosalpha * (-tgalpha) * (-sin alpha )}{-sinalpha *tg alpha} = cos alpha$