Question

chứng minh rằng : sin\(^4\)x+cos\(^4\)x=1 - 2cos\(^2\)x.sin\(^2\)x

Answer 1

\(sin^4\left(x\right)+cos^4\left(x\right)+2sin^2\left(x\right)cos^2\left(x\right)=\left[sin^2\left(x\right)+cos^2\left(x\right)\right]^2=1^2=1\\ \Rightarrow sin^4\left(x\right)+cos^4\left(x\right)=1-2sin^2\left(x\right)cos^2\left(x\right)\left(đpcm\right)\)

Answer 2

sin^4x+cos^4x

=(sin^2x+cos^2x)^2-2*sin^2x*cos^2x

=1-2*cos^2x*sin^2x