Verify the Identity 1/(tan(x))+1/(cot(x))=tan(x)+cot(x)

Problem

1/tan(x)+1/cot(x)=tan(x)+cot(x)

Solution

1. Identify the reciprocal identities for the trigonometric functions involved.

2. Apply the identity cot(x)=1/tan(x) to the first term on the left side of the equation.

3. Apply the identity tan(x)=1/cot(x) to the second term on the left side of the equation.

4. Substitute these values back into the expression to see that the left side is equivalent to the right side.

5. Rearrange the terms to match the exact order of the right side of the identity.

Final Answer

1/tan(x)+1/cot(x)=tan(x)+cot(x)

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