Solve for x csc(x)*cos(x)=cot(x)

Problem

csc(x)*cos(x)=cot(x)

Solution

1. Identify the trigonometric identities for the functions involved in the equation.

2. Substitute the reciprocal identity csc(x)=1/sin(x) into the left side of the equation.

3. Multiply the terms on the left side to combine them into a single fraction.

1/sin(x)⋅cos(x)=cos(x)/sin(x)

4. Apply the quotient identity cot(x)=cos(x)/sin(x) to compare both sides.

5. Observe that the left side simplifies exactly to the right side, meaning the equation is an identity.

6. Determine the domain constraints, as the expression is undefined where sin(x)=0

sin(x)≠0⇒x≠n*π

Final Answer

csc(x)*cos(x)=cot(x)

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