Download D.C. L 6.3 Proving Trigonometric Identities

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MA L 7.2 Verifying Trigonometric
Identities
Make the left side equal the right.
Hints for Proving Identities
• Select the more complex side of the = sign to work on.
• Use double & half-angle formulas is necessary to get all trig
functions of the same angle (x)
• Carry out any algebraic manipulations, such as adding, subtracting,
multiplying, or factoring.
• If given rational expressions, get LCD.
• Converting all expressions to sines and cosines is often helpful.
• If working on the left side, constantly refer to the right and see how
you can get something on the left to match the right.
• Try Something! Put your pencil to work and get involved. There is
usually more than one method. If you find your equation getting
further complicated, start over with a new approach.
Let’s begin with what we already know.
The Pythagorean theorem yields…
Here are three KEY techniques:
Replacing
Replacing
sin x with 1  cos x
2
2
cos2 x with 1  2sin x
Using the Quadratic Formula
2
1=1
Example 333
3