求证cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)=2cosα-3tanα

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求证cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)=2cosα-3tanα

求证cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)=2cosα-3tanα
求证cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)=2cosα-3tanα

求证cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)=2cosα-3tanα
证明:cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)
=cosα(2/cosα+sinα/cosα)(1/cosα-2sinα/cosα)
=cosα*(2+sina)/cosα*(1-2sina)/cosα
=(2-3sina-2(sina)^2)/cosα
=(2-3sina-2(cona)^2)/cosα
=(2(cosα)^2)-3sina)/cosα
=2cosα-3tanα.
所以原式成立.

左边=cos(720°+α)(2/cosα+tanα)(1/cosα-2tanα)
=cosα(2/cosα+tanα)(1/cosα-2tanα)
=cosα*(2+sina)/cosa*(1-2sina)/cosa
=(2+sina)(1-2sina)/cosa
=(2-3sina-2sin^2a)/cosa
=(2cos^2a-3sina)/cosa
=2cosa-3tana
=右边