LHS=left hand side, RHS=right hand side
LHS=(tanx)/(1+secx) +(1+secx)/tanx =tanx1+secx+1+secxtanx
=((tanx)(tanx)+(1+secx)(1+secx))/(tanx(1+secx))=(tanx)(tanx)+(1+secx)(1+secx)tanx(1+secx)
=(tan^2x+1+2secx+sec^2x)/(tanx(1+secx))=tan2x+1+2secx+sec2xtanx(1+secx)
=((tan^2x+1)+2secx+sec^2x)/(tanx(1+secx))=(tan2x+1)+2secx+sec2xtanx(1+secx)
=(sec^2x +2secx+sec^2x)/(tanx (1+secx))=sec2x+2secx+sec2xtanx(1+secx)
=(2sec^2x+2secx)/(tanx(1+secx))=2sec2x+2secxtanx(1+secx)
=(2secx(secx+1))/(tanx(1+secx))=2secx(secx+1)tanx(1+secx)
=2 secx/tanx=2secxtanx
=2 (1/cosx)/(sinx/cosx)=21cosxsinxcosx
=2 1/cosx xx cosx/sinx=21cosx×cosxsinx
=2 1/sinx=21sinx
=2cscx=2cscx
=RHS=RHS