Solve for x 8cos(x)^2=4

Problem

8*cos(x)=4

Solution

1. Isolate the squared trigonometric term by dividing both sides of the equation by 8

cos(x)=4/8

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

cos(x)=1/2

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

cos(x)=±√(,1/2)

4. Rationalize the denominator to express the value in a standard form.

cos(x)=±1/√(,2)

cos(x)=±√(,2)/2

5. Identify the angles on the unit circle where the cosine value is √(,2)/2 or −√(,2)/2

x=π/4,(3*π)/4,(5*π)/4,(7*π)/4

6. Generalize the solution to include all possible rotations by adding multiples of π since these points are separated by 90 or π/2 increments.

x=π/4+(n*π)/2

Final Answer

x=π/4+(n*π)/2,n∈ℤ

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