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

The general solution for tan(x)-cot(x)=2cot^2(x) is x=0.98930…+pin

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

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

x = 0.98930 \dots + πn

Solution steps

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

Subtract

2 cot^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) \approx 0.65729 \dots

cot (x) = 0.65729 \dots : x = arccot (0.65729 \dots) + πn

Combine all the solutions

x = arccot (0.65729 \dots) + πn

Show solutions in decimal form

x = 0.98930 \dots + πn

cot (\frac{- x + 3 n}{4}) = 0

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

\frac{cos ( a )}{1 + sin ( a )} = sec (a)

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

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

What is the general solution for tan(x)-cot(x)=2cot^2(x) ?
The general solution for tan(x)-cot(x)=2cot^2(x) is x=0.98930…+pin