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

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

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tan^2(x)-cot(x)=0

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

x = \frac{π}{4} + πn

Solution steps

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

Rewrite using trig identities

- cot (x) + \frac{1}{cot ^{2} ( x )} = 0

Solve by substitution

cot (x) = 1, cot (x) = - \frac{1}{2} + i \frac{3}{2}, cot (x) = - \frac{1}{2} - i \frac{3}{2}

cot (x) = 1 : x = \frac{π}{4} + πn

cot (x) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

cot (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

x = \frac{π}{4} + πn

5 sec^{3} (x) - 20 sec (x) = 0

3 cot^{2} (x) - 1 = 0, x

cos^{2} (x) + cos (2 x) = 0

- 2 sin (θ) + 3 cos (2 θ) = 0

sin^{2} (x) - 4 = 0

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