Verify the Identity (sin(x))/(tan(x))=cos(x)

Problem

sine x over tangent x equals cosine x

Solution

1. Identify the trigonometric identity for the tangent function.

tangent x equals sine x over cosine x

2. Substitute the identity for tangent x into the denominator of the left side of the equation.

the fraction with numerator sine x and denominator sine x over cosine x

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

sine x times cosine x over sine x

4. Cancel the common factor of sine x from the numerator and the denominator.

cosine x

5. Conclude that the left side has been transformed to match the right side.

cosine x equals cosine x

Final Answer

sine x over tangent x equals cosine x

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