Question

Упростить -sin²b*cos²b+cos²b-cos⁴b

Answer 1

-sin²b*cos²b+cos²b-cos⁴b=cos²b*(-sin²b)+cos²b*1+cos²b*(-cos²b)=cos²b(-sin²b+1-cos²b)=cos²b*0=0

Answer 2

$-sin^2a\cdot cos^2a+cos^2a-cos^4a=\\\\=-sin^2a\cdot cos^2a+cos^2a\cdot (\underbrace {1-cos^2a}_{sin^2a})=\\\\=\underbrace {-sin^2a\cdot cos^2a}+\underbrace {cos^2a\cdot sin^2a}=0$