Verify the Identity sin(2x)=2sin(x)

Problem

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

Solution

1. Identify the double angle formula for the sine function, which states that sin(2*x) is equivalent to sin(x+x)

2. Apply the angle sum identity for sine, sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B) where A=x and B=x

3. Substitute the values into the identity to get sin(x+x)=sin(x)*cos(x)+cos(x)*sin(x)

4. Combine the like terms on the right side of the equation, as sin(x)*cos(x) and cos(x)*sin(x) are identical.

Final Answer

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

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