求证1+sina+cosa分之sin2a=sina+cosa-1 求指点呀!

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求证1+sina+cosa分之sin2a=sina+cosa-1 求指点呀!
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求证1+sina+cosa分之sin2a=sina+cosa-1 求指点呀!
求证1+sina+cosa分之sin2a=sina+cosa-1 求指点呀!

求证1+sina+cosa分之sin2a=sina+cosa-1 求指点呀!
sin2a / (1+sina+cosa)
=2sinacosa / (2sina/2cosa/2 +2cos^2 a/2)
=4sina/2cosa/2 cosa / [2cosa/(sina/2+cosa/2)]
=2sina/2(cos^2 a/2-sin^2 a/2) / (sina/2+cosa/2)
=2sina/2(cosa/2-sina/2)
=2sina/2cosa/2 -2sin^2 a/2
=sina+cosa-1

sin(2a)=(1+sina+cosa)(sina+cosa-1)右边=(sina+cosa)的平方减1=1+2sinacosa-1=2sinacosa=sin(2a)