(2cos^2a-1)/( sina-cosa)

Решите задачу:

$\frac{2cos^2a-1}{sina-cosa}=\\\\\star \; \; cos2a=cos^2a-sin^2a=cos^2a-(1-cos^2a)=2cos^2a-1\; \; \star \\\\=\frac{cos^2a-sin^2a}{sina-cosa} =\frac{(cosa-sina)(cosa+sina)}{-(cosa-sina)}=cosa+sina\\\\\\P.S.\; \; cosa+sina=cosa+cos( \frac{\pi }{2}-a)=2\cdot \underbrace {cos\frac{\pi }{4}}_{\frac{\sqrt2}{2}}\cdot cos(a-\frac{\pi }{4})=\\\\=\sqrt2\cdot cos(a-\frac{\pi }{4} )$