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