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已知tan^2阿尔法=2tan^2贝塔+1,求证:sin^2贝塔=2sin^2阿尔法-1
人气:186 ℃ 时间:2020-02-03 12:14:51
解答
tan^2α=2tan^2β+1
sin^2α/cos^2α=2sin^2β/cos^2β+1
sin^2αcos^2β=2sin^2βcos^2α+cos^2αcos^2β
sin^2α(1-sin^2β)=2sin^2β(1-sin^2α)+(1-sin^2α)(1-sin^2β)
化简得:
sin^2贝塔=2sin^2阿尔法-1
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