What is the general solution for sqrt(3)tan(x/4)+5=4 ?

The general solution for sqrt(3)tan(x/4)+5=4 is x=(10pi)/3+4pin

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sqrt(3)tan(x/4)+5=4

3 tan (\frac{x}{4}) + 5 = 4

x = \frac{10 π}{3} + 4 πn

Solution steps

3 tan (\frac{x}{4}) + 5 = 4

Move

5

to the right side

3 tan (\frac{x}{4}) = - 1

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{5 π}{6} + πn

Solve

\frac{x}{4} = \frac{5 π}{6} + πn : x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

2 sin (3 x) = 1

sin (4 x) = cos (2 x)

cot^{2} (θ) - cot (θ) = 0

5 cos (2 θ) = - 15 cos (θ) - 10

2 cos (x) - 5 = 3 sec (x)

What is the general solution for sqrt(3)tan(x/4)+5=4 ?
The general solution for sqrt(3)tan(x/4)+5=4 is x=(10pi)/3+4pin