Simplify tan(-x)cos(-x)

Problem

tan(−x)*cos(−x)

Solution

1. Apply even-odd identities to the trigonometric functions. The tangent function is odd, so tan(−x)=−tan(x) The cosine function is even, so cos(−x)=cos(x)

tan(−x)=−tan(x)

cos(−x)=cos(x)

2. Substitute these identities back into the original expression.

(−tan(x))*(cos(x))

3. Use the quotient identity for tangent, which states that tan(x)=sin(x)/cos(x)

−sin(x)/cos(x)⋅cos(x)

4. Simplify the expression by canceling the common factor of cos(x) in the numerator and denominator.

−sin(x)

Final Answer

tan(−x)*cos(−x)=−sin(x)

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