Simplify tan(-x)

Problem

tan(−x)

Solution

1. Identify the parity of the tangent function. The tangent function is defined as the ratio of the sine function to the cosine function.

tan(−x)=sin(−x)/cos(−x)

2. Apply the odd-even identities for sine and cosine. Recall that sin(x) is an odd function, meaning sin(−x)=−sin(x) and cos(x) is an even function, meaning cos(−x)=cos(x)

tan(−x)=(−sin(x))/cos(x)

3. Simplify the expression by recognizing the definition of the tangent function within the fraction.

tan(−x)=−(sin(x)/cos(x))

tan(−x)=−tan(x)

Final Answer

tan(−x)=−tan(x)

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