Question

Sin^2 theta + cos^4 theta=sos^2theta + sin^4 theta
Proove

Answer 1

sin^2θ+cos^2θ=1 can be rearranged into sin^2θ=1−cos^2θ and cos^2θ=1−sin^2θ

We can see that: cos^4θ=(cos^2θ)(cos^2θ)=(1−sin^2θ)(1−sin^2θ)=1−2sin^2θ+sin^4θ

sin^2θ+cos^4θ=cos^2θ+sin^4θ

sin^2θ+(1−2sin^2θ+sin^4θ)=cos^2θ+sin^4θ

sin^2θ+1−2sin^2θ+sin^4θ=cos^2θ+sin^4θ

sin^4θ−sin^2θ+1=cos^2θ+sin^4θ

sin^4θ−(1−cos^2θ)+1=cos^2θ+sin^4θ

sin^4θ−1+cos^2θ+1=cos^2θ+sin^4θ

sin^4θ+cos^2θ=cos^2θ+sin^4θ