Learn How To Do It

To prove a trigonometric identity,
-Simplify one or both sides of an equation so that they are equal.
-When solving DO NOT cross over the equal sign.
-Know the fundamental Pythagorean identities.

There are many different approaches one can take when solving such problems, to use the shortest method possible keep these things in mind:
1. Try to stay on one side, and start with the side that has addition or subtraction.
2. Simplify terms as much as possible. Look out for:
  • fractions or like terms that can be combined
  • anything that can be factored in order to simply the expression (difference of two terms or perfect square trinomials.
  • denominators that can be mulitipied by the conjugate
  • Algebreic expressions that can be distributed, squared or multiplied.
3. Change trig functions to Sin and Cos.

Some Examples Of Proofs:

Proof: cscx = cotx/cosx

Step 1: Equation becomes: cscx = cosx/cosxsinx
*The cot(x) was changed to cos(x) over sin(x)
Step 2: Equation becomes: cscx = 1/sinx
*Cos(x) over Cos(x) cancle and change to just one.
Step 3: Equation becomes: cscx = cscx
*One over Sin(x) is the same as Csc(x)

ALWAYS write out the entire equation for each step of the process

Let's Practice

Let's Review

The video below is a different way to prove a trigonometric identity, but it still works. It's an interesting way to look at proving identities!

Use this link for more practice: http://www.algebralab.org/practice/practice.aspx?file=Trigonometry_BasicTrigIdentities.xml