证明恒等式cota^2-cosa^2=cota^2cosa^2cota^2-cosa^2=cota^2cosa^2 (sina-csca)(cosa-seca)=1/(tana+cota)

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证明恒等式cota^2-cosa^2=cota^2cosa^2cota^2-cosa^2=cota^2cosa^2 (sina-csca)(cosa-seca)=1/(tana+cota)

证明恒等式cota^2-cosa^2=cota^2cosa^2cota^2-cosa^2=cota^2cosa^2 (sina-csca)(cosa-seca)=1/(tana+cota)
证明恒等式cota^2-cosa^2=cota^2cosa^2
cota^2-cosa^2=cota^2cosa^2 (sina-csca)(cosa-seca)=1/(tana+cota)

证明恒等式cota^2-cosa^2=cota^2cosa^2cota^2-cosa^2=cota^2cosa^2 (sina-csca)(cosa-seca)=1/(tana+cota)
一,
cota^2-cosa^2
=cosa^2/sina^2-cosa^2
=(cosa^2-cosa^2sina^2)/sina^2
=cosa^2(1-sina^2)/sina^2
=cosa^2cosa^2/sina^2
=cota^2cosa^2

(sina-csca)(cosa-seca)
=(sina-1/sina)(cosa-1/cosa)
=[(sina^2-1)/sina][(cosa^2-1)/cosa]
=(cosa^2/sina)(sina^2/cosa)
=sinacosa
而1/(tana+cota)
=1/[(sina/cosa)+(cosa/sina)]
=1/[(sina^2+cosa^2)/cosasina]
=cosasina/(sina^2+cosa^2)
=cosasina
所以(sina-csca)(cosa-seca)=1/(tana+cota)

切割化炫即可

1.
cot^2a-cos^2a
=cos^2a/sin^2a - cos^2a
=cos^2a*(1/sin^2a - 1)
=cos^2a*(1-sin^2a)/sin^2a
=cos^2a*(cos^2a/sin^2a)
=cot^2a*cos^2a
2.
(sina-csca)(cosa-seca)
=(sina-1/...

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1.
cot^2a-cos^2a
=cos^2a/sin^2a - cos^2a
=cos^2a*(1/sin^2a - 1)
=cos^2a*(1-sin^2a)/sin^2a
=cos^2a*(cos^2a/sin^2a)
=cot^2a*cos^2a
2.
(sina-csca)(cosa-seca)
=(sina-1/sina)*(cosa-1/cosa)
=sinacosa+1/(sinacosa)-sina/cosa-cosa/sina
=sinacosa+1/(sinacosa)-sin^2a/(sinacosa)-cos^2a/(sinacosa)
=sinacosa
=1 / 1/sinacosa
=1 / (sin^2a+cos^2a)/(sinacosa)
=1 / (sina/cosa + cosa/sina)
=1 / (tana+cota)
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