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VERIFYING TRIGONOMETRIC IDENTITIES Example 1: Verify the identity Let's assume that the left side of the identity is the "more complicated" one. Therefore, we will try to change it to look like the right side. What could we do to the left side? 1. 2. 3. 4. 5. Add or subtract trigonometric expressions? NO Multiply trigonometric expressions? NO Factor trigonometric expressions? NO Separate rational trigonometric expressions? NO Use fundamental identities to rewrite an expression? YES Let's change cot x to sines and cosines as follows: and then we multiply Now what could we do? 1. 2. 3. 4. 5. Add or subtract trigonometric expressions? YES Multiply trigonometric expressions? NO Factor trigonometric expressions? NO Separate rational trigonometric expressions? NO Use fundamental identities to rewrite an expression? NO Let's use the common denominator sin x What now? 1. 2. 3. 4. 5. Add or subtract trigonometric expressions? NO Multiply trigonometric expressions? NO Factor trigonometric expressions? NO Separate rational trigonometric expressions? NO Use fundamental identities to rewrite an expression? YES Given the Pythagorean Identity and given the Reciprocal Identity the right side because , we can write , we can show that the left side equals