Solve for x 16cos(x)^2-4=0

Problem

16*cos(x)−4=0

Solution

1. Isolate the squared trigonometric term by adding 4 to both sides of the equation.

16*cos(x)=4

2. Divide both sides by 16 to further isolate the squared term.

cos(x)=4/16

3. Simplify the fraction on the right side of the equation.

cos(x)=1/4

4. Take the square root of both sides, remembering to include both the positive and negative roots.

cos(x)=±√(,1/4)

cos(x)=±1/2

5. Determine the values of x that satisfy cos(x)=1/2 and cos(x)=−1/2 within one full rotation (0≤x<2*π.

x=π/3,(2*π)/3,(4*π)/3,(5*π)/3

6. Generalize the solution to include all possible values of x by adding multiples of π since the solutions are spaced π apart.

x=π/3+n*π

x=(2*π)/3+n*π

Final Answer

x=π/3+n*π,(2*π)/3+n*π

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