Question

3) sin^4 x – cos^4 x = 0,5;​

Answer 1

Ответ:

Что это такоеЖыныма тиеди

Answer 2

To solve the equation sin^4(x) - cos^4(x) = 0.5, we can use the trigonometric identity:

sin^2(x) - cos^2(x) = 1

Let's rewrite the equation using this identity:

(sin^2(x) - cos^2(x))(sin^2(x) + cos^2(x)) = 0.5

(sin^2(x) - cos^2(x))(1) = 0.5

sin^2(x) - cos^2(x) = 0.5

Now, using the trigonometric identity sin^2(x) + cos^2(x) = 1, we have:

1 - cos^2(x) - cos^2(x) = 0.5

2cos^2(x) = 0.5

cos^2(x) = 0.25

Taking the square root of both sides:

cos(x) = ±0.5

To find the possible values of x, we need to consider the cosine function's periodicity. The cosine function has a period of 2π. Therefore, the solutions will repeat every 2π.

The solutions for x can be obtained by finding the angles whose cosine is 0.5 or -0.5. Using the inverse cosine function (arccos), we have:

For cos(x) = 0.5: x = arccos(0.5) ≈ 60° + 360°k or x = -arccos(0.5) ≈ 300° + 360°k

For cos(x) = -0.5: x = arccos(-0.5) ≈ 120° + 360°k or x = -arccos(-0.5) ≈ 240° + 360°k

Here, k is an integer that represents the number of times the solutions repeat every 2π.

So, the solutions for the equation sin^4(x) - cos^4(x) = 0.5 are:

x ≈ 60° + 360°k, x ≈ 300° + 360°k, x ≈ 120° + 360°k, x ≈ 240° + 360°k, where k is an integer.