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

Problem

sin(x)/tan(x)=cos(x)

Solution

1. Identify the trigonometric identity for the tangent function.

tan(x)=sin(x)/cos(x)

2. Substitute the identity for tan(x) into the denominator of the left side of the equation.

sin(x)/sin(x)/cos(x)

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

sin(x)⋅cos(x)/sin(x)

4. Cancel the common factor of sin(x) from the numerator and the denominator.

cos(x)

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

cos(x)=cos(x)

Final Answer

sin(x)/tan(x)=cos(x)

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