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

Problem

tan(x)*cos(x)=sin(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 left side of the equation.

sin(x)/cos(x)⋅cos(x)

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

sin(x)

4. Conclude that the left side of the equation is equal to the right side.

sin(x)=sin(x)

Final Answer

tan(x)*cos(x)=sin(x)

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