What is the general solution for 5cot^2(x)-15=0 ?

The general solution for 5cot^2(x)-15=0 is x= pi/6+pin,x=(5pi)/6+pin

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5cot^2(x)-15=0

5 cot^{2} (x) - 15 = 0

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

5 cot^{2} (x) - 15 = 0

Solve by substitution

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

sin (x) = \frac{2}{5}

csc (x) = 5

sec^{2} (x) + tan^{2} (x) - 1 = 0

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x < 2 π

tan (θ) = 10

What is the general solution for 5cot^2(x)-15=0 ?
The general solution for 5cot^2(x)-15=0 is x= pi/6+pin,x=(5pi)/6+pin