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

Problem

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

Solution

1. Identify the double angle identities for the numerator and the denominator.

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

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

4. Simplify the denominator by combining the constants.

1+(2*cos2(x)−1)=2*cos2(x)

5. Divide the numerator by the denominator.

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

6. Cancel the common factors of 2 and cos(x)

sin(x)/cos(x)

7. Apply the quotient identity sin(x)/cos(x)=tan(x) to complete the verification.

Final Answer

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

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