Question

упростите выражение
-sin^2B-cos^2B+cos^2B-cos^4B

Answer 1

$-sin^2 \beta \underbrace {-cos^2\beta +cos^2\beta }_{0}-cos^4 \beta = -(\underbrace {1-cos^2\beta }_{sin^2\beta })-cos^4 \beta =\\\\=-1+cos^2 \beta -cos^4\beta =-1+cos^2 \beta \cdot (1-cos^2 \beta )=\\\\=-1+cos^2\beta \cdot sin^2 \beta =-1+(sin \beta \cdot cos \beta )^2=\\\\=-1+(\frac{1}{2}\cdot sin2 \beta )^2=\frac{1}{4}\, sin^2\, 2 \beta -1$