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

The general solution for 3=tan^2(x) is x= pi/3+pin,x=(2pi)/3+pin

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3=tan^2(x)

3 = tan^{2} (x)

x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn

Degrees

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

Solution steps

3 = tan^{2} (x)

Switch sides

tan^{2} (x) = 3

Solve by substitution

tan^{2} (x) = 3

Let:

tan (x) = u

u^{2} = 3

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

u^{2} = 3

For

x^{2} = f (a)

the solutions are

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

u = 3, u = - 3

Substitute back

u = tan (x)

tan (x) = 3, tan (x) = - 3

tan (x) = 3, tan (x) = - 3

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 3

General solutions for

tan (x) = 3

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = - 3

General solutions for

tan (x) = - 3

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

Combine all the solutions

x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn

tan (θ) csc (θ) + 2 tan (θ) = 0

250 = 88 sin (θ) + 242 cos (θ)

4 + 2 csc (\frac{θ}{2}) = 8

2 cos (3 x) = \frac{1}{2}, x = \frac{17 π}{4}

cos (θ) = sin (3 6^{\circ})

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