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

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

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

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

1

from both sides

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

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

6 cos^{2} (x) - 5 sin (x) + 5 = 0

1 + cos^{2} (a) = 3 sin (x) cos (x)

3 cos (x) + sin (x) = cos (x) - 2 sin (x)

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

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