Simplify sin(2x)+cos(x)

Problem

sin(2*x)+cos(x)

Solution

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

2. Substitute the identity into the original expression.

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

3. Factor out the common term cos(x) from both parts of the expression.

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

Final Answer

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

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