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

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

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1=-cot^2(x)+2

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

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Switch sides

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

Solve by substitution

cot (x) = 1, cot (x) = - 1

cot (x) = 1 : x = \frac{π}{4} + πn

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

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

60 \cdot \frac{π}{180} = 2 arctan (\frac{x}{17})

sin (a) = - \frac{1}{8}, \frac{3 π}{2} \leq a \leq 2 π

3 cos^{2} (x) - 23 cos (x) = sin^{2} (x)

sin (x) + cos (x) = \frac{3}{2}

cos^{2} (x) - sin^{2} (x) - 5 sin (x) = 3

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