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

Problem

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

Solution

1. Apply half-angle identities to rewrite the numerator and denominator in terms of x/2

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

3. Substitute 1+cos(x)=2*cos^2(x/2) into the denominator using the power-reduction identity.

4. Simplify the fraction by canceling the common factor of 2*cos(x/2) from both the numerator and the denominator.

5. Identify the resulting trigonometric ratio as the tangent function.

Final Answer

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

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