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

Problem

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

Solution

1. Identify the angle addition formula for the sine function, which states sin(α+β)=sin(α)*cos(β)+cos(α)*sin(β)

2. Rewrite the expression sin(2*x) by expressing the double angle as a sum of two identical angles, x+x

3. Substitute α=x and β=x into the angle addition formula.

4. Apply the formula to get sin(x+x)=sin(x)*cos(x)+cos(x)*sin(x)

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

Final Answer

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

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