Question

Ctg(п/5+4x)=1 tg(п/4+x)+1=0

Answer 1

Используем частные случаи.

Answer 2

It looks like you have a system of two trigonometric equations involving the tangent function (tg). Let's solve these equations step by step.

1. The first equation is: ctg(π/5 + 4x) = 1

   To solve this equation, first find the angle whose cotangent is 1: ctg(θ) = 1 implies θ = π/4

   So, π/5 + 4x = π/4

   Now, solve for x: π/5 + 4x = π/4

   Subtract π/5 from both sides: 4x = π/4 - π/5

   Find a common denominator: 4x = (5π - 4π) / 20

   Simplify the right side: 4x = π / 20

   Now, divide by 4: x = π / (4 * 20) x = π / 80

2. The second equation is: tg(π/4 + x) + 1 = 0

   Subtract 1 from both sides: tg(π/4 + x) = -1

   To find x, you need to find the angle whose tangent is -1. The angle π/4 + x should be in the second or fourth quadrant where the tangent is negative. In these quadrants, the tangent of an angle is equal to the negative of the tangent of its supplementary angle. Therefore:

   π/4 + x = -π/4 + kπ (k is an integer)

   Now, solve for x: x = -π/2 + kπ - π/4

   You can simplify this expression further if needed, depending on the range of values you want for x.

So, the solutions to the system of equations are: x₁ = π/80 x₂ = -π/2 + kπ - π/4 (where k is an integer)