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

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

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tan^2(x)=cot(x)

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

cot (x)

from both sides

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

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

tan^{2} (θ) = 0

tan (a) = \frac{7}{8}

\frac{sec ( x ) sin ( x )}{tan ( x ) cot ( x )} = sin^{2} (x)

tan (θ) = - \frac{3}{1}

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