Question

доказать тождество sin4a+cos4a*ctg2a=ctg2a

Answer 1

$\displaystyle sin4a+cos4a*ctg2a=2sin2a*cos2a+cos4a*\frac{cos2a}{sin2a}=\\\\=cos2a(2sin2a+\frac{cos^22a-sin^22a}{sin2a})=cos2a*(\frac{2sin^22a+cos^22a-sin^22a}{sin2a})=\\\\=\frac{cos2a*(sin^22a+cos^22a)}{sin2a}= \frac{cos2a*1}{sin2a}=ctg2a$