Solve for x 2cos(x)sin(x)-cos(x)=0

Problem

2*cos(x)*sin(x)−cos(x)=0

Solution

1. Factor out the common term cos(x) from the left side of the equation.

cos(x)*(2*sin(x)−1)=0

2. Apply the zero product property by setting each factor equal to zero.

cos(x)=0

2*sin(x)−1=0

3. Solve for x in the first equation cos(x)=0

x=π/2+n*π

4. Isolate the sine term in the second equation 2*sin(x)−1=0

2*sin(x)=1

sin(x)=1/2

5. Solve for x in the equation sin(x)=1/2 using the unit circle.

x=π/6+2*n*π

x=(5*π)/6+2*n*π

Final Answer

x=π/2+n*π,π/6+2*n*π,(5*π)/6+2*n*π

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