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

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

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

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

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Solve by substitution

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

Let:

cot (x) = u

u^{2} = u^{2} - 2 u

u^{2} = u^{2} - 2 u : u = 0

u^{2} = u^{2} - 2 u

Subtract

u^{2}

from both sides

u^{2} - u^{2} = u^{2} - 2 u - u^{2}

Simplify

0 = - 2 u

Switch sides

- 2 u = 0

Divide both sides by

- 2

- 2 u = 0

Divide both sides by

- 2

\frac{- 2 u}{- 2} = \frac{0}{- 2}

Simplify

u = 0

u = 0

Substitute back

u = cot (x)

cot (x) = 0

cot (x) = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{2} + πn

cos (x) = \frac{4}{10}

16 cos (2 x) - 4 = 0

- csc (x) cot (x) = 0

4 sin (θ) = \frac{1}{cos ( θ )}

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

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