Solve for x 2-3cos(x)=5+3cos(x)

Problem

2−3*cos(x)=5+3*cos(x)

Solution

1. Group the cosine terms by adding 3*cos(x) to both sides of the equation.

2=5+6*cos(x)

2. Isolate the term with cosine by subtracting 5 from both sides.

−3=6*cos(x)

3. Solve for cosine by dividing both sides by 6

cos(x)=−3/6

4. Simplify the fraction to find the value of the trigonometric function.

cos(x)=−1/2

5. Identify the general solution for x by finding the angles where the cosine is −1/2 This occurs in the second and third quadrants.

x=(2*π)/3+2*π*n

x=(4*π)/3+2*π*n

Final Answer

x=(2*π)/3+2*π*n,(4*π)/3+2*π*n

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