[tex](sin^{2} \alpha -tg^{2} \alpha )*cos^2\alpha[/tex]упростите выражение. Created by fqqwqqf. algebra-ru

tex]упростите выражение...

Erasyllla

Объяснение:

$({ \sin( \alpha ) }^{2} + \frac{ { \sin( \alpha ) }^{2} }{ { \cos( \alpha ) }^{2} } ) { \cos( \alpha ) }^{2} \\( \frac{ { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} ) } { { \cos( \alpha ) }^{2} ?} ) { \cos( \alpha ) }^{2} \\ { \sin( \alpha ) }^{2} ( { \cos( \alpha ) }^{2} + 1) \\ { \sin( \alpha ) }^{4}$

0 votes Thanks 0

sangers1959

Объяснение:

$(sin^2\alpha -tg^2\alpha )*cos^2\alpha =(sin^2\alpha -\frac{sin^2\alpha }{cos^2\alpha } )*cos^2\alpha =-sin^2\alpha *(\frac{1}{cos^2\alpha} -1)*cos^2\alpha =\\ =-sin^2\alpha*\frac{1-cos^2\alpha }{cos^2\alpha } *cos^2\alpha =-sin^2\alpha *sin^2\alpha =-sin^4\alpha .$

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