Question

(sin^3(a-270)*cos(360-a))/(tg^3(a-90)*cos^2(a-270))



Пожалуйста, помогите упростить

Answer 1

$\frac{sin^3( \alpha -270)*cos(360- \alpha )}{tg^3( \alpha -90)*cos^2( \alpha -270)} =$$\frac{-sin^3( 270-\alpha)*cos(360- \alpha )}{-tg^3( 90-\alpha)*cos^2( 270-\alpha)} =$$\frac{sin^3( 270-\alpha)*cos(360- \alpha )}{tg^3( 90-\alpha)*cos^2( 270-\alpha)} =$$= \frac{-cos^3 \alpha *cos \alpha }{ctg^3 \alpha *sin^2 \alpha } = \frac{-cos^4 \alpha }{ \frac{cos^3 \alpha }{sin^3 \alpha }*sin^2 \alpha } = \frac{-cos^4 \alpha*sin \alpha }{cos^3 \alpha } =-cos \alpha *sin \alpha =- \frac{1}{2} sin2 \alpha$