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

Problem

cos(x)+2*sin(x)*cos(x)=0

Solution

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

cos(x)*(1+2*sin(x))=0

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

cos(x)=0

1+2*sin(x)=0

3. Solve for x in the first equation cos(x)=0 by identifying where the cosine function is zero on the unit circle.

x=π/2+n*π

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

2*sin(x)=−1

sin(x)=−1/2

5. Solve for x in the equation sin(x)=−1/2 by identifying the angles in the third and fourth quadrants.

x=(7*π)/6+2*n*π

x=(11*π)/6+2*n*π

Final Answer

cos(x)+2*sin(x)*cos(x)=0⇒x=π/2+n*π,(7*π)/6+2*n*π,(11*π)/6+2*n*π

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