Verify the Identity cot(x)=(1+cos(2x))/(sin(2x))

Problem

cot(x)=(1+cos(2*x))/sin(2*x)

Solution

1. Identify the double angle identities for the terms on the right side of the equation.

2. Substitute the identity cos(2*x)=2*cos2(x)−1 into the numerator to eliminate the constant term.

3. Substitute the identity sin(2*x)=2*sin(x)*cos(x) into the denominator.

4. Simplify the numerator by combining 1 - 1$.

(1+(2*cos2(x)−1))/(2*sin(x)*cos(x))

5. Reduce the expression by canceling the common factors of 2 and cos(x) from the numerator and denominator.

(2*cos2(x))/(2*sin(x)*cos(x))

6. Apply the quotient identity cos(x)/sin(x)=cot(x) to reach the final form.

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

Final Answer

cot(x)=(1+cos(2*x))/sin(2*x)

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