Question

2cos(x+п/6)=корень из 2​

Answer 1

Ответ:

2cos(x+π/6)=$\sqrt{2}$

cos(x+π/6)=$\sqrt{2}$/ 2

cos (2π - ( x+ π/6)) = $\sqrt{2}$/ 2

cos (11π/6 - x) = $\sqrt{2}$/ 2

x+π/6 = π/4

11π /6 - x = π/4

x = не является числом

Answer 2

To solve the equation 2cos(x+π/6) = √2, we can start by isolating the cosine term.

Divide both sides of the equation by 2 to obtain:

cos(x + π/6) = √2 / 2

Since cos(π/4) = √2 / 2, we can rewrite the equation as:

cos(x + π/6) = cos(π/4)

To solve for x, we can set the arguments of the cosine functions equal to each other:

x + π/6 = π/4

Now, subtract π/6 from both sides of the equation:

x = π/4 - π/6

To simplify the right side, we need to find a common denominator:

x = (3π/12 - 2π/12) / 1

x = π/12

Therefore, the solution to the equation 2cos(x+π/6) = √2 is x = π/12.