Question

Упростите: sin2a*ctg2a:(1-sin2a)

Answer 1

$sin2 \alpha *ctg2 \alpha :(1-sin2 \alpha ) = \frac{sin2 \alpha }{1} * \frac{cos2 \alpha }{sin2 \alpha } :(1-2sin \alpha cos \alpha )=$$\frac{ cos2 \alpha }{ cos^{2} \alpha +sin^2 \alpha -2sin \alpha cos \alpha }= \frac{cos^2 \alpha -sin^2 \alpha }{ (cos \alpha -sin \alpha )^{2} } =$$\frac{(cos \alpha -sin \alpha )(cos \alpha +sin \alpha )}{(cos \alpha -sin \alpha )(cos \alpha -sin \alpha )}= \frac{cos \alpha +sin \alpha }{cos \alpha -sin \alpha }$