Question 737632
{{{1/(1-cosx)-1/(1+secx) = csc^2x+cot^2x}}}

LHS = {{{1/(1-cosx)-1/(1+secx) }}}


Take LCD 

{{{1/(1-cosx)-1/(1+(1/cosx))) }}}



{{{1/(1-cosx)-1/((1+cosx)/cosx)) }}}



{{{1/(1-cosx)-cosx/(1+cosx)}}}


{{{(1+cosx-cosx(1-cosx))/((1+cosx)(1-cosx))}}}


{{{(1+cos^2(x))/(1-cos^2(x))}}}


{{{(1+cos^2(x))/(sin^2(x))}}}


{{{1/sin^2(x)+cos^2(x)/sin^2(x)}}}



{{{cosec^2x+cot^2x}}}

LHS = RHS