Question

Cos(sinx)=корень 2/2

Answer 1

Sinx=π/4 u sinx=-π/4
x=arcsin(π/4)+2πk U x=π-arcsin(π/4)+2πk U x=-arcsin(π/4)+2πk U 
x=-π-arcsin(π/4)+2πk,k∈z

Answer 2

The equation you've provided is:

cos(sin(x)) = √2/2

Let's solve for x.

To find the value of x, we can take the inverse cosine (also known as the arccosine) of both sides since cos and arccos are inverse functions. This will give us:

x = arccos(√2/2)

Now, we need to find the angle whose cosine is √2/2. In trigonometry, we know that:

cos(π/4) = √2/2

So, the value of x is:

x = π/4

Remember that there are infinitely many solutions to the equation because the cosine function is periodic. The general solution for x is:

x = π/4 + 2nπ (where n is an integer)

For example, other solutions include:

x = π/4 + 2π (n = 1) x = π/4 + 4π (n = 2) and so on.