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

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

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tan(x)=2-cot(x)

tan (x) = 2 - cot (x)

x = \frac{π}{4} + πn

Solution steps

tan (x) = 2 - cot (x)

Subtract

2 - cot (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = 1

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn

cosh^{2} (x) - 10 cosh (x) + 25 = 0

6 cos (x) + 1 = 4

sin (θ) = cos (3 7^{\circ})

cot (x) - cot (x) csc (x) = 0

3 sin^{2} (x) - 3 sin (x) + cos^{2} (x) = 0

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