Solve for x sin(x)cos(x)=1/4

Problem

sin(x)*cos(x)=1/4

Solution

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

2. Multiply both sides of the original equation by 2 to match the identity.

2*sin(x)*cos(x)=2⋅1/4

3. Substitute the identity into the left side of the equation.

sin(2*x)=1/2

4. Find the general solutions for the angle 2*x where the sine value is 1/2

2*x=π/6+2*k*π

2*x=(5*π)/6+2*k*π

5. Divide by 2 to solve for x where k is any integer.

x=π/12+k*π

x=(5*π)/12+k*π

Final Answer

sin(x)*cos(x)=1/4⇒x=π/12+k*π,(5*π)/12+k*π

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