(1+cos^2α)tan^2α-(1/cos^2α)

问题描述:

(1+cos^2α)tan^2α-(1/cos^2α)
1个回答 分类:数学 2014-12-16

问题解答:

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原式=(1+cos^2a)sin^2a/cos^2a-(1/cos^2a)
=(sin^2a+sin^2acos^2a-1)/cos^2a(注意到1=sin^2a+cos^2a,有sin^2a-1=-cos^2a)
=(sin^2acos^2a-cos^2a)/cos^2a
=[cos^2a(sin^2a-1)]/cos^2a
=sin^2a-1
=-cos^2a
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