Question

2sina-sin2a/cos2a-1 -ctga​

Answer 1

$\frac{2sina-sin2a}{cos2a-1}-ctga=\frac{2sina-2\, sina\, cosa}{(cos^2a-sin^2a)-(sin^2a+cos^2a)}-ctga=\frac{2\, sina\cdot (1-cosa)}{-2sin^2a}-ctga=\\\\=-\frac{1-cosa}{sina}-ctga=-\frac{2sin^2\frac{a}{2}}{2\, sin\frac{a}{2}\, cos\frac{a}{2}}-ctga=-\frac{sin\frac{a}{2}}{cos\frac{a}{2}}-ctga=-tg\frac{a}{2}-ctga\\\\ili\\\\...=-\frac{1-cosa}{sina}-\frac{cosa}{sina}=\frac{-1+cosa-cosa}{sina}=-\frac{1}{sina}$