Trigonometry/Verifying Trigonometric Identities

To verify an identity means to make sure that the equation is true by setting both sides equal to one another.

There is no set method that can be applied to verifying identities; there are, however, a few different ways to start based on the identity which is to be verified.

Introduction

Trigonometric identities are used in both course texts and in real life applications to abbreviate trigonometric expressions. It is important to remember that merely verifying an identity or altering an expression is not an end in itself, but rather that identities are used to simplify expressions according to the task at hand. Trigonometric expressions can always be reduced to sines and cosines, which are more managable than their inverse counterparts.

To verify an identity:

1) Always try to reduce the larger side first.

2) Sometimes getting all trigonometric functions on one side can help.

3) Remember to use and manipulate already existing identities. The Pythagorean identities are usually the most useful in simplifying.

4) Remember to factor if needed.

5) Whenever you have a squared trigonometric function such as Sin^2(t), always go to your pythagorean identities, which deal with squared functions.

Easy example $1/cot(t)=sin(t)/cos(t)$

1/cot(t)= tan(t) ,so $tan(t)=sin(t)/cos(t)$

tan(t) is the same as sint(t)/cos(t) and therefore can be rewritten as $sin(t)/cos(t)=sin(t)/cos(t)$

Identity verified