prove that tan-1 ( cosx /1-sinx) - cot -1( whole root 1+cosx/1-cosx) = pi/4

LHS=tan-1cosx1-sinx-cot-11+cosx1-cosx=tan-1cos2x2-sin2x2cos2x2+sin2x2-2sinx2cosx2-cot-12cos2x22sin2x2=tan-1cosx2+sinx2cosx2-sinx2cosx2-sinx22-cot-1cotx2=tan-1cosx2+sinx2cosx2-sinx2-x2=tan-1cosx2cosx2+sinx2cosx2cosx2cosx2-sinx2cosx2-x2=tan-11+tanx21-tanx2-x2=tan-1tanπ4+tanx21-tanπ4×tanx2-x2=tan-1π4+x2-x2=π4+x2-x2=π4=RHSHence, proved.

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