Question

Cos2x+sin^2 x=0.75 помогите пожалуйста, обьясните как это решается

Answer 1

1) раскрываем двойной угол:
cos2x = cos^2(x)-sin^2(x)
2) решаем уравнение:
cos^2(x)-sin^2(x)+sin^2(x)=0,75
cos^2(x)=3/4
a) cos(x)=корень из 3/2
х=плюс минус п/6 + 2пk, k € z
Ответ: плюс минус п/6 + 2пk, k € z

Answer 2

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Answer 3

Solving the Equation Cos(2x) + Sin^2(x) = 0.75

To solve the equation Cos(2x) + Sin^2(x) = 0.75, we can use trigonometric identities and algebraic manipulation to simplify and solve for the variable x.

First, let's use the double-angle identity for cosine: Cos(2x) = 1 - 2Sin^2(x). We can substitute this into the original equation to get:

1 - 2Sin^2(x) + Sin^2(x) = 0.75

Simplify the equation:

1 - Sin^2(x) = 0.75

Now, we can solve for Sin^2(x):

Sin^2(x) = 1 - 0.75

Sin^2(x) = 0.25

Taking the square root of both sides, we get:

Sin(x) = ±√0.25

Sin(x) = ±0.5

So, Sin(x) can be either 0.5 or -0.5.

Now, let's find the values of x that satisfy these conditions.

Using the inverse sine function, we can find the angles for which Sin(x) equals 0.5 or -0.5.

The solutions for Sin(x) = 0.5 are x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.

The solutions for Sin(x) = -0.5 are x = 7π/6 + 2πn and x = 11π/6 + 2πn, where n is an integer.

These are the solutions for the equation Cos(2x) + Sin^2(x) = 0.75.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.