What is the general solution for cot^2(x)-3=0 ?

The general solution for cot^2(x)-3=0 is x= pi/6+pin,x=(5pi)/6+pin

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cot^2(x)-3=0

cot^{2} (x) - 3 = 0

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

cot^{2} (x) - 3 = 0

Solve by substitution

cot^{2} (x) - 3 = 0

Let:

cot (x) = u

u^{2} - 3 = 0

u^{2} - 3 = 0 : u = 3, u = - 3

u^{2} - 3 = 0

Move

3

to the right side

u^{2} - 3 = 0

Add

3

to both sides

u^{2} - 3 + 3 = 0 + 3

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

tan (θ) = - 2

sec (x) + 1 = 0

sin (2 x) = - sin (x)

\frac{sin ( x )}{2} + \frac{sin ( x )}{3} = \frac{1}{4}

2 cos (x) sin (x) - cos (x) = 0

What is the general solution for cot^2(x)-3=0 ?
The general solution for cot^2(x)-3=0 is x= pi/6+pin,x=(5pi)/6+pin