Simplify (sin(2x))/(1+cos(2x))

Problem

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

Solution

1. Apply the double angle identity for the numerator using sin(2*x)=2*sin(x)*cos(x)

2. Apply the double angle identity for the denominator using cos(2*x)=2*cos2(x)−1

3. Simplify the denominator by combining the terms 1+(2*cos2(x)−1)

1+2*cos2(x)−1=2*cos2(x)

4. Substitute the expressions back into the fraction.

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

5. Cancel the common factors of 2 and cos(x) from the numerator and the denominator.

sin(x)/cos(x)

6. Use the tangent identity to rewrite the resulting expression.

tan(x)

Final Answer

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

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