To solve the given equation, let's first substitute ctg 2x as y:
y = ctg 2x
Now, the equation becomes:
y² - 6y + 5 = 0
This is a quadratic equation that can be factored as:
(y - 5)(y - 1) = 0
Setting each factor to zero gives us the solutions for y:
y = 5 or y = 1
Now, substitute back y = ctg 2x:
ctg 2x = 5 or ctg 2x = 1
To solve for x, we need to find the angles whose cotangent values are 5 and 1. The values are not standard angles, so we'll use the inverse cotangent function to find the solutions:
For ctg 2x = 5 2x = arccot(5 x = (1/2)arccot(5)
For ctg 2x = 1 2x = arccot(1 2x = π/ x = π/8
Therefore, the solutions to the equation ctg²2x - 6ctg 2x + 5 = 0 are x = (1/2)arccot(5) and x = π/8.
To solve the given equation, let's first substitute ctg 2x as y:
y = ctg 2x
Now, the equation becomes:
y² - 6y + 5 = 0
This is a quadratic equation that can be factored as:
(y - 5)(y - 1) = 0
Setting each factor to zero gives us the solutions for y:
y = 5 or y = 1
Now, substitute back y = ctg 2x:
ctg 2x = 5 or ctg 2x = 1
To solve for x, we need to find the angles whose cotangent values are 5 and 1. The values are not standard angles, so we'll use the inverse cotangent function to find the solutions:
For ctg 2x = 5
2x = arccot(5
x = (1/2)arccot(5)
For ctg 2x = 1
2x = arccot(1
2x = π/
x = π/8
Therefore, the solutions to the equation ctg²2x - 6ctg 2x + 5 = 0 are x = (1/2)arccot(5) and x = π/8.