求证sina(1+sina)+cosa(1+1/tana)=1/sina + 1/cosa

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求证sina(1+sina)+cosa(1+1/tana)=1/sina+1/cosa求证sina(1+sina)+cosa(1+1/tana)=1/sina+1/cosa求证sina(1+sina)

求证sina(1+sina)+cosa(1+1/tana)=1/sina + 1/cosa
求证sina(1+sina)+cosa(1+1/tana)=1/sina + 1/cosa

求证sina(1+sina)+cosa(1+1/tana)=1/sina + 1/cosa
左边=sina(1+sina/cosa)+cosa(1+cosa/sina)
=sina+sina^2/cosa+cosa+cosa^2/sina
=(sina^2+cosa^2)/sina+(sina^2+cosa^2)/cosa
=1/sina + 1/cosa