What is the general solution for cot^2(x)= 1/3 ?

The general solution for cot^2(x)= 1/3 is x=1.04719…+pin,x=2.09439…+pin

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cot^2(x)= 1/3

cot^{2} (x) = \frac{1}{3}

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

Degrees

x = 6 0^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

cot^{2} (x) = \frac{1}{3}

Solve by substitution

cot^{2} (x) = \frac{1}{3}

Let:

cot (x) = u

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

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

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

For

x^{2} = f (a)

the solutions are

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

u = \frac{1}{3}, u = - \frac{1}{3}

Substitute back

u = cot (x)

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{3}

cot (x) = \frac{1}{3}, cot (x) = - \frac{1}{3}

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

cot (x) = \frac{1}{3}

Apply trig inverse properties

cot (x) = \frac{1}{3}

General solutions for

cot (x) = \frac{1}{3}

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (\frac{1}{3}) + πn

x = arccot (\frac{1}{3}) + πn

cot (x) = - \frac{1}{3} : x = arccot (- \frac{1}{3}) + πn

cot (x) = - \frac{1}{3}

Apply trig inverse properties

cot (x) = - \frac{1}{3}

General solutions for

cot (x) = - \frac{1}{3}

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- \frac{1}{3}) + πn

x = arccot (- \frac{1}{3}) + πn

Combine all the solutions

x = arccot (\frac{1}{3}) + πn, x = arccot (- \frac{1}{3}) + πn

Show solutions in decimal form

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

2 sin (θ) = 1 - 2 cos (θ)

cot (3 x) = 0

4 sin (x) + csc (x) = 0

sec (\frac{θ}{2}) = 2

3 csc^{2} (θ) = 1 + 2 csc^{2} (θ)

What is the general solution for cot^2(x)= 1/3 ?
The general solution for cot^2(x)= 1/3 is x=1.04719…+pin,x=2.09439…+pin