(sinα)^6+(cosα)^6+3*(sinα)^2*(cosα)^2好了，大題怎么我做著都沒有思路……5…………

熱心網友

(sinα)^6+(cosα)^6+3*(sinα)^2*(cosα)^2= [(sinα)^2 +(cosα)^2]*[(sinα)^4 -(sinαcosα)^2 +(cosα)^4]+3*(sinα)^2*(cosα)^2= 1*{[(sinα)^2 +(cosα)^2]^2 - 3*(sinα)^2*(cosα)^2}+3*(sinα)^2*(cosα)^2= 1-3*(sinα)^2*(cosα)^2+3*(sinα)^2*(cosα)^2=1

熱心網友

=(sin^2α+cos^2α)(sin^4α-sin^2α*cos^2α+cos^4α)+3*sin^2α*cos^2α=1