Respuesta :

osikbro

Answer:

[tex]\dfrac{\pi}{4},\dfrac{3\pi}{4}[/tex]

Step-by-step explanation:

[tex]2\sin^2(\theta)=1[/tex]

Divide both sides by 2:

[tex]\sin^2(\theta)=\dfrac{1}{2}[/tex]

Take the square root of both sides:

[tex]\sin(\theta)=\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]

The only two places on the unit circle where the y value of the point is [tex]\dfrac{\sqrt{2}}{2}[/tex] are at:

[tex]\dfrac{\pi}{4},\dfrac{3\pi}{4}[/tex]

Hope this helps!

π/4 , 3π/4 is the solution of the given equation

What is Trigonometric Equations

The equations that involve the trigonometric functions of a variable are called trigonometric equations. In the upcoming discussion, we will try to find the solutions to such equations. These equations have one or more trigonometric ratios of unknown angles. For example, cos x -sin2 x = 0, is a trigonometric equation that does not satisfy all the values of x. Hence for such equations, we have to find the values of x or find the solution.

According to the question

2[tex]sin^{2}[/tex]θ = 1

Divide both sides by 2:

[tex]sin^{2}[/tex]θ = 1/2

Take the square root of both sides:

sinθ = 1/[tex]\sqrt{2}[/tex] = [tex]\sqrt{2}[/tex]/2

The only two places on the unit circle where the y value of the point is  are at:

π/4 , 3π/4

Hence,π/4 , 3π/4 is the solution of the given equation

To learn more about Trigonometric Equations from here

https://brainly.in/question/47923065

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