Kindly answer this determinants Q

Solution 
LHS
A=1tanx-tanx1AT=1-tanxtanx1A=1+tan2x=sec2x.A-1=1A1-tanxtanx1=1sec2x1-tanxtanx1AT×A-1=1sec2x1-tanxtanx1×1-tanxtanx1=1sec2x1-tan2x-2tanx2tanx1-tan2x=1-tan2xsec2x-2tanxsec2x2tanxsec2x1-tan2xsec2x=cos2x-sin2xcos2xsec2x-2tanxsec2x2tanxsec2xcos2x-sin2xcos2xsec2x=cos2x-2sinxcosx2sinxcosxcos2x=cos2x-sin2xsin2xcos2x=RHS

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