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 xx 22 cos1 with sin Replacing 2cos2 with 1 2sinx xUsing the Quadratic Formula

1=1

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Example 3