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.

2. Substitute the identity tan(x)=sin(x)/cos(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. Compare the simplified left side to the right side of the original equation to confirm they are equal.

sin(x)=sin(x)

Final Answer

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

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