Simplify tan(x)+cos(-x)+tan(-x)

Problem

tan(x)+cos(−x)+tan(−x)

Solution

1. Apply even-odd identities for the trigonometric functions.

2. Recall that cosine is an even function, meaning cos(−x)=cos(x)

3. Recall that tangent is an odd function, meaning tan(−x)=−tan(x)

4. Substitute these identities into the original expression: tan(x)+cos(x)−tan(x)

5. Combine like terms by canceling tan(x) and −tan(x)

Final Answer

tan(x)+cos(−x)+tan(−x)=cos(x)

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