Prove that sinQ cotQ + sinQ cosecQ = 1 + cosQ

Here we have to prove sinQ cotQ + sinQ cosecQ = 1 + cosQ we will start with LHS (Left hand side ie sinQ cotQ + sinQ cosecQ ) and prove that it is equal to 1 + cosQ Hence we will get LHS = RHS

Proof

Lets start with LHS of the equations
LHS = sinQ cotQ + sinQ cosecQ
= sinQ (cosQ/sinQ) + sinQ * 1/sinQ

= cosQ + 1
= 1 + cosQ