化简sin^4α+cos^4α+1/2sin²2α=?

问题描述:

化简sin^4α+cos^4α+1/2sin²2α=?

sin^4α+cos^4α+1/2sin²2α
=(sin^2α+cos^2α)²-2sin²αcos²α+1/2sin²2α
=1-1/2(2sinαcosα)²+1/2sin²2α
=1-1/2sin²2α+1/2sin²2α
=1