Solve for x 4sin(x)^2-2=0

Problem

4*sin2(x)−2=0

Solution

1. Isolate the trigonometric term by adding 2 to both sides of the equation.

4*sin2(x)=2

2. Divide both sides by 4 to solve for the squared sine function.

sin2(x)=2/4

3. Simplify the fraction on the right side.

sin2(x)=1/2

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

sin(x)=±√(,1/2)

5. Rationalize the denominator to find the standard values for the sine function.

sin(x)=±1/√(,2)

sin(x)=±√(,2)/2

6. Identify the angles x within the interval [0,2*π) that satisfy the equation.

x=π/4,(3*π)/4,(5*π)/4,(7*π)/4

7. Generalize the solution by adding multiples of π since the values are spaced π/2 apart.

x=π/4+(n*π)/2

Final Answer

x=π/4+(n*π)/2

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