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

Problem

sin(x)*cot(x)=cos(x)

Solution

1. Identify the trigonometric identity for the cotangent function.

cot(x)=cos(x)/sin(x)

2. Substitute the identity into the left side of the equation.

sin(x)⋅cos(x)/sin(x)

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

cos(x)

4. Compare the simplified left side to the right side of the original equation to confirm they are equal.

cos(x)=cos(x)

Final Answer

sin(x)*cot(x)=cos(x)

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