What is the general solution for -4cot^2(x)=1+2cot(x)-3cot^2(x) ?

The general solution for -4cot^2(x)=1+2cot(x)-3cot^2(x) is x=(3pi)/4+pin

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-4cot^2(x)=1+2cot(x)-3cot^2(x)

- 4 cot^{2} (x) = 1 + 2 cot (x) - 3 cot^{2} (x)

x = \frac{3 π}{4} + πn

Solution steps

- 4 cot^{2} (x) = 1 + 2 cot (x) - 3 cot^{2} (x)

Solve by substitution

cot (x) = - 1

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

cos (x) (2 sin (x) - 2) = 0

2 sin^{2} (θ) - 3 sin (θ) = - 1

4 cos^{2} (θ) + 2 = 3

cos (kπ) = 0

What is the general solution for -4cot^2(x)=1+2cot(x)-3cot^2(x) ?
The general solution for -4cot^2(x)=1+2cot(x)-3cot^2(x) is x=(3pi)/4+pin