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已知a属于(0,π),sina+cosa=1/5.求①sina*cosa②sina-cosa③tan(a-π/2)
人气:428 ℃ 时间:2020-10-01 21:32:20
解答
(sina+cosa)^2=1/25
2sinacosa=1/25-sin^2+cos^2=-24/25
sinacosa=-12/25
(sina-cosa)^2=sin^2+cos^2-2sinacosa
                       =49/25
因为a∈(0,π)所以sina<cosa
sina-cosa=-7/5
tan(a-π/2)=tana
sina+cosa=1/5
               
sina-cosa=-7/5
合并sina=-3/5,cosa=4/5
tana=sina/cosa=-3/4
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