三角函数化简sin^6α+cos^6α+3sin^2α*cos^2α=?急_数学解答

三角函数化简sin^6α+cos^6α+3sin^2α*cos^2α=?急

人气：410 ℃　时间：2019-09-30 20:32:17

解答

由sin^2a+cos^2a=1
原式=(sin^2a+cos^2a)(sin^4a-sin^2acos^2a+cos^4a)+3sin^2acos^2a
=sin^4a-sin^2acos^2a+cos^4a+3sin^2acos^2a
=sin^4a+2sin^2acos^2a+cos^4a
=(sin^2a+cos^2a)2
=1