Solve for x 2cos(x)^2+ square root of 3cos(x)=0

Problem

2*cos2(x)+√(,3)*cos(x)=0

Solution

1. Identify the common factor in the terms of the equation. Both terms contain cos(x)

2. Factor out the greatest common factor, which is cos(x) to rewrite the equation as a product.

cos(x)*(2*cos(x)+√(,3))=0

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

cos(x)=0

2*cos(x)+√(,3)=0

4. Solve the first equation for x The cosine function is zero at odd multiples of π/2

x=π/2+n*π

5. Solve the second equation for cos(x) by subtracting √(,3) and dividing by 2

2*cos(x)=−√(,3)

cos(x)=−√(,3)/2

6. Find the values of x where cos(x)=−√(,3)/2 This occurs in the second and third quadrants.

x=(5*π)/6+2*n*π

x=(7*π)/6+2*n*π

Final Answer

x=π/2+n*π,(5*π)/6+2*n*π,(7*π)/6+2*n*π

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