sin α+sin^2α=1,则cos^2 α+cos^6 α+cos^8α=多少?,

题目

sin α+sin^2α=1,则cos^2 α+cos^6 α+cos^8α=多少?,

答案

sin α+sin^2α=1,cos^2α+sin^2α=1,由此两式可知sin α=cos^2α,则所求式可化为sin α+sin^3α+sin^4α,提取公因式后该式=sin α+sin^2α(sin α+sin^2α)=sin α+sin^2α=1.纯手打,