Question

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

Answer 1

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

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

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

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

$cos2x=cos2x$