求证:sin a(1+tan a)+cos a(1+1/tan a)=1/sin a+1/cos a

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

求证:sin a(1+tan a)+cos a(1+1/tan a)=1/sin a+1/cos a
求证:sin a(1+tan a)+cos a(1+1/tan a)=1/sin a+1/cos a

求证:sin a(1+tan a)+cos a(1+1/tan a)=1/sin a+1/cos a
sin a(1+tan a)+cos a(1+1/tan a)
=sina+sina*tana+cosa+cosa/tana
=(sina+cos^2(a)/sina)+(cosa+sin^2(a)/cosa)
=(sin^2(a)+cos^2(a))/sina+(cos^2(a)+sin^2(a))/cosa
=1/sin a+1/cos a