Solve for x 2sin(2x)^2=1

Problem

2*sin2(2*x)=1

Solution

1. Isolate the squared trigonometric term by dividing both sides of the equation by 2

sin2(2*x)=1/2

2. Take the square root of both sides to solve for the sine function, remembering to include both the positive and negative roots.

sin(2*x)=±√(,1/2)

3. Rationalize the denominator to identify the standard values on the unit circle.

sin(2*x)=±√(,2)/2

4. Determine the general solutions for the argument 2*x where the sine value is √(,2)/2 or −√(,2)/2 These occur at odd multiples of π/4

2*x=π/4+(n*π)/2

5. Solve for x by dividing the entire expression by 2

x=π/8+(n*π)/4

Final Answer

x=π/8+(n*π)/4,n∈ℤ

Want more problems? Check here!