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

Problem

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

Solution

1. Identify the trigonometric identity for the double angle of sine, which states that 2*sin(x)*cos(x)=sin(2*x)

2. Substitute the identity into the expression to replace the product term.

3. Identify the Pythagorean identity 1=sin2(x)+cos2(x) if an alternative form is required, but the most concise simplified form uses the double angle.

4. Combine the terms to reach the final simplified expression.

Final Answer

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

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