Question

Cos ( x/4 - п/3) = 1​

Answer 1

$\cos \left( \dfrac{x}{4} - \dfrac{\pi }{3} \right) = 1\\\\ \dfrac{x}{4} - \dfrac{\pi }{3} = 2\pi n\\\\ \dfrac{x}{4} = \dfrac{\pi }{3} + 2\pi n\\\\x= \dfrac{4\pi }{3} + 8\pi n, \ n\in \mathbb{Z}$

Ответ: $\dfrac{4\pi}{3}+8\pi n$, где n - целые числа

Answer 2

To solve the equation cos(x/4 - π/3) = 1, we can use the property of the cosine function that states cos(θ) = 1 when θ = 2πn, where n is an integer.

Let's simplify the equation step by step:

cos(x/4 - π/3) = 1

Since cos(θ) = 1, we can write:

x/4 - π/3 = 2πn

Now, let's solve for x:

x/4 = 2πn + π/3

Multiply both sides of the equation by 4 to isolate x:

x = 8πn + 4π/3

The solution to the equation cos(x/4 - π/3) = 1 is given by x = 8πn + 4π/3, where n is an integer.