求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)

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求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)求证:1/sin2x+1/tan2x+1/sinx=1/

求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)
求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)

求证:1/sin2x+1/tan2x+1/sinx=1/tan(x/2)
1/sin2x+1/tan2x+1/sinx
=1/2sinxcosx+(1-tan²x)/2tanx+1/sinx
=(1+cos²x-sin²x+2cosx)/2sinxcosx
=(2cos²x+2cosx)/2sinxcosx
=(cosx+1)/sinx
=2cos²(x/2)/2sin(x/2)cos(x/2)
=cos(x/2)/sin(x/2)
=1/tan(x/2)