What is the general solution for 3-2cot^2(x)=-cot^2(x) ?

The general solution for 3-2cot^2(x)=-cot^2(x) is x= pi/6+pin,x=(5pi)/6+pin

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3-2cot^2(x)=-cot^2(x)

Solution

3 - 2 cot^{2} (x) = - cot^{2} (x)

Solution

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

3 - 2 cot^{2} (x) = - cot^{2} (x)

Solve by substitution

3 - 2 cot^{2} (x) = - cot^{2} (x)

Let:

cot (x) = u

3 - 2 u^{2} = - u^{2}

3 - 2 u^{2} = - u^{2} : u = 3, u = - 3

3 - 2 u^{2} = - u^{2}

Move

3

to the right side

3 - 2 u^{2} = - u^{2}

Subtract

3

from both sides

3 - 2 u^{2} - 3 = - u^{2} - 3

Simplify

- 2 u^{2} = - u^{2} - 3

- 2 u^{2} = - u^{2} - 3

Move

u^{2}

to the left side

- 2 u^{2} = - u^{2} - 3

Add

u^{2}

to both sides

- 2 u^{2} + u^{2} = - u^{2} - 3 + u^{2}

Simplify

- u^{2} = - 3

- u^{2} = - 3

Divide both sides by

- 1

- u^{2} = - 3

Divide both sides by

- 1

\frac{- u ^{2}}{- 1} = \frac{- 3}{- 1}

Simplify

u^{2} = 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

Substitute back

u = cot (x)

cot (x) = 3, cot (x) = - 3

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 3

General solutions for

cot (x) = 3

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}{6} + πn

x = \frac{π}{6} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

cot (x) = - 3

General solutions for

cot (x) = - 3

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{5 π}{6} + πn

x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Popular Examples

2cos(t)+1=0

2 cos (t) + 1 = 0

sin(3x)= 1/(sqrt(2))

sin (3 x) = \frac{1}{2}

tan^2(θ)=-tan(θ)

tan^{2} (θ) = - tan (θ)

sec(θ)=-2/(sqrt(3))

sec (θ) = - \frac{2}{3}

tan(θ)= 8/12

tan (θ) = \frac{8}{12}

Frequently Asked Questions (FAQ)

What is the general solution for 3-2cot^2(x)=-cot^2(x) ?
The general solution for 3-2cot^2(x)=-cot^2(x) is x= pi/6+pin,x=(5pi)/6+pin