Question

Решить уравнение1) cos(x+П/3)=1

Answer 1

x+π/3=2πn

x=-π/3+2πn

частный случай

Answer 2

To solve the equation cos(x + π/3) = 1, you can follow these steps:

Step 1: Identify the trigonometric identity for cos(θ) = 1. Step 2: Set the argument (x + π/3) equal to that value and solve for x. Step 3: Account for multiple solutions in the trigonometric cycle.

Let's proceed with the solution:

Step 1: The trigonometric identity for cos(θ) = 1 is: cos(θ) = 1 when θ = 2nπ, where n is an integer.

Step 2: Set the argument (x + π/3) equal to 2nπ: x + π/3 = 2nπ

Step 3: Solve for x: x = 2nπ - π/3

Since n is an integer, there are infinitely many solutions for x. You can express the general solution as follows:

x = 2nπ - π/3, where n is an integer.

This means that for each integer value of n, you will get a different solution for x that satisfies the original equation. The solutions are equally spaced apart due to the periodic nature of trigonometric functions.