9.3B  Proving Trig Identities

How to Prove Trig Identities

  The first thing to remember -

          ~  You need to prove that the left side equals the right side.

         ~  You are NOT solving equations, so don't solve for x.

         ~  You cannot subtract/add/multiply/divide the left from the right or right from the left.

         ~  Think of the equals sign as a wall you cannot cross over.

         ~  You need to simplify one side of the identity at a time.

   Helpful hints when proving identities

           ~   Start with the side containing the more complicated expression.

          ~   Rewrite sums or differences of quotients as a single quotient - find the common denominator.

          ~   Sometimes rewriting one side in terms of sine and/or cosine functions only will help.

          ~   Always keep your goal in mind ---> simplify so both sides are equal.

          ~   As you manipulate one side of the expression, keep in mind the expression on the other side.