Question

$frac{2sin {}^{2} alpha }{tg2 alpha times tg alpha } = cos {}^{2} alpha - sin {}^{2} alpha :$
Докажите тождество:

Answer 1

$frac{2sin^2a}{frac{sin2x}{cos2x}*frac{sinx}{cosx}} = cos2x$

$frac{2sin^2x}{frac{2sinxcosx}{cos2x}*frac{sinx}{cosx}} =cos2x$

$frac{2sin^2x}{frac{2sinx}{cos2x}*sinx } =cos2x$

$frac{2sinx}{frac{2sinx}{cos2x} } =cos2x$

$cos2x=cos2x$