Question

If 3cot² x - 5cot x = -2, then cot x = _____.

Answer 1

To solve 3cot² x - 5cot x = -2 for cot x, rearrange the equation as a quadratic equation, and solve it using the quadratic formula.

Step-by-step explanation:

To solve the equation 3cot² x - 5cot x = -2 for cot x, we can rearrange the equation as a quadratic equation:

Let’s substitute cot x = y, the equation becomes:

3y² - 5y = -2

Now, we can solve this quadratic equation.

Using the quadratic formula: y = (-b ± sqrt(b² - 4ac)) / 2a, where a = 3, b = -5, and c = 2, we can substitute these values into the formula:

y = (-(-5) ± sqrt((-5)² - 4(3)(-2))) / (2(3))

y = (5 ± sqrt(25 + 24)) / 6

y = (5 ± sqrt(49)) / 6

y = (5 ± 7) / 6

Therefore, cot x = (5 + 7) / 6 or cot x = (5 - 7) / 6

So, cot x = 2 or cot x = -1/3