Question

помогите пожалуйста , упростить выражение )))​ 100 баллов

Answer 1

$1) (1-\cos(-\alpha))(1+\cos(-\alpha))=1-\cos^2(-\alpha)=sin^2(-\alpha )=sin^2\alpha$

$2) tg(\alpha)ctg(-\alpha )+\cos^2\alpha = -tg(\alpha)ctg(\alpha )+\cos^2\alpha=-1+\cos^2\alpha=-sin^2\alpha$

$3) \sin(-\alpha )-\sin\alpha \cdot ctg^2(-\alpha )= -\sin(\alpha )-\sin\alpha \cdot ctg^2(\alpha ) = -\sin\alpha (1+ctg^2(\alpha )) = -\sin\alpha (1+\frac{\cos^2\alpha }{\sin^2\alpha }) = -\sin\alpha \cdot \frac{\sin^2\alpha +\cos^2\alpha }{\sin^2\alpha } = -\sin\alpha \cdot \frac{1 }{\sin^2\alpha } = \frac{-1}{\sin\alpha }$

$4) \frac{1+\cos(-\alpha )}{sin(-\alpha )} - ctg(-\alpha )= \frac{1+\cos(\alpha )}{-sin(\alpha )} + ctg(\alpha ) = \frac{1+\cos(\alpha )}{-sin(\alpha )} + \frac{\cos\alpha }{\sin\alpha } = \frac{-1}{\sin\alpha }$

$5) \frac{\sin^2(-\alpha )-sin^4(-\alpha )}{\cos^2(-\alpha )} = \frac{\sin^2(\alpha )-sin^4(\alpha )}{\cos^2(\alpha )}=\frac{\sin^2\alpha (1-\sin^2\alpha )}{\cos^2\alpha }=\frac{\sin^2\alpha \cos^2\alpha }{\cos^2\alpha }=\sin^2\alpha$