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

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

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2tan(x)-sqrt(3)=tan(x)

2 tan (x) - 3 = tan (x)

x = \frac{π}{3} + πn

Degrees

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

Solution steps

2 tan (x) - 3 = tan (x)

Solve by substitution

2 tan (x) - 3 = tan (x)

Let:

tan (x) = u

2 u - 3 = u

2 u - 3 = u : u = 3

2 u - 3 = u

Move

3

to the right side

2 u - 3 = u

Add

3

to both sides

2 u - 3 + 3 = u + 3

Simplify

2 u = u + 3

2 u = u + 3

Move

u

to the left side

2 u = u + 3

Subtract

u

from both sides

2 u - u = u + 3 - u

Simplify

u = 3

u = 3

Substitute back

u = tan (x)

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

Combine all the solutions

x = \frac{π}{3} + πn

4 tan^{2} (x) - 1 = 0

2 sin (θ) cos (θ) = cos (θ)

7 cos (x) = 5 cos (x) + 3

sin (α) = - \frac{3}{5}, π < α < \frac{3 π}{2}

cos^{4} (x) - sin^{4} (x) = 0

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