Question

化简cos4α+sin2αcos2α+sin2α

2、4是二次方，四次方的意思

Answer 1

(cosα)^4+(sinαcosα)^2+(sinα)^2

=(cosα)^2.((cosα)^2+(sinα)^2)+(sinα)^2
=(cosα)^2+(sinα)^2
=1

追问

不明白第二步是怎么来的。。。

追答

(cosα)^4+(sinαcosα)^2+(sinα)^2
=[(cosα)^4+(sinαcosα)^2]+(sinα)^2
==(cosα)^2.[ (cosα)^2+(sinα)^2]+(sinα)^2

Answer 2

cos^4α+sin²αcos²α+sin²α
=cos²α(cos²α+sin²α)+sin²α
=cos²α+sin²α
=1