What is the general solution for 19cot^2(x)-19=0 ?

The general solution for 19cot^2(x)-19=0 is x= pi/4+pin,x=(3pi)/4+pin

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19cot^2(x)-19=0

19 cot^{2} (x) - 19 = 0

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

Solution steps

19 cot^{2} (x) - 19 = 0

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

θ, 2 sin (θ) = csc (θ) + 1

sin^{2} (x) \cdot 2 cos (x) = 2

cos (θ) = \frac{20}{27}

32 cos (x) + 2 = - 1

\frac{1}{sin ( x ) \cdot cos ( x ) + cos ( x )} = \frac{1}{cos ( x )}

What is the general solution for 19cot^2(x)-19=0 ?
The general solution for 19cot^2(x)-19=0 is x= pi/4+pin,x=(3pi)/4+pin