What is the general solution for 3tan(x/4)-sqrt(3)=0 ?

The general solution for 3tan(x/4)-sqrt(3)=0 is x=(2pi)/3+4pin

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3tan(x/4)-sqrt(3)=0

3 tan (\frac{x}{4}) - 3 = 0

x = \frac{2 π}{3} + 4 πn

Solution steps

3 tan (\frac{x}{4}) - 3 = 0

Move

3

to the right side

3 tan (\frac{x}{4}) = 3

Divide both sides by

3

tan (\frac{x}{4}) = \frac{3}{3}

General solutions for

tan (\frac{x}{4}) = \frac{3}{3}

\frac{x}{4} = \frac{π}{6} + πn

Solve

\frac{x}{4} = \frac{π}{6} + πn : x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

sin^{2} (3 x) = 1

2 - - 1 - 6 sin (x) = - 4 sin (x)

2 sin (\frac{x}{2}) - 1 = 0

cos^{2} (x) - sin^{2} (x) + sin (x) = 0

2 tan^{2} (t) = - 3 sec (t)

What is the general solution for 3tan(x/4)-sqrt(3)=0 ?
The general solution for 3tan(x/4)-sqrt(3)=0 is x=(2pi)/3+4pin