What is the general solution for tan^2(x)= 1/(cot(x)) ?

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

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tan^2(x)= 1/(cot(x))

tan^{2} (x) = \frac{1}{cot ( x )}

x = \frac{π}{4} + πn

Solution steps

tan^{2} (x) = \frac{1}{cot ( x )}

Subtract

\frac{1}{cot ( x )}

from both sides

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

Simplify

tan^{2} (x) - \frac{1}{cot ( x )} : \frac{tan ^{2} ( x ) cot ( x ) - 1}{cot ( x )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

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

Multiply both sides by

cot (x)

- cot (x) + 1 = 0

Move

1

to the right side

- cot (x) = - 1

Divide both sides by

- 1

cot (x) = 1

Verify Solutions

Find undefined (singularity) points:

cot (x) = 0

Combine undefined points with solutions:

cot (x) = 1

General solutions for

cot (x) = 1

x = \frac{π}{4} + πn

\frac{sin ( θ )}{cos ( θ )} = 3

48 sin^{2} (x) = 48 - 24 cos (x)

1 - 4 cos (2 x) = 0

\frac{1}{2} = cos (θ)

tan^{2} (x) + 5 tan (x) = 0

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