Prove the following trigonometric identities:
cot A−cos Acot A+cos A=cosec A−1cosec A+1
LHS=cot A−cos Acot A+cos A
=cosAsinA−cosAcosAsinA+cosA
=cosecAcosA−cosAcosecAcosA+cosA
=cosA(cosecA−1)cosA(cosecA+1)
=cosecA−1cosecA+1
=RHS