What is the general solution for 5+2tan(3θ+pi/3)=3 ?

The general solution for 5+2tan(3θ+pi/3)=3 is θ=(pin)/3+(5pi)/(36)

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5+2tan(3θ+pi/3)=3

5 + 2 tan (3 θ + \frac{π}{3}) = 3

θ = \frac{πn}{3} + \frac{5 π}{36}

Solution steps

5 + 2 tan (3 θ + \frac{π}{3}) = 3

Move

5

to the right side

2 tan (3 θ + \frac{π}{3}) = - 2

Divide both sides by

2

tan (3 θ + \frac{π}{3}) = - 1

General solutions for

tan (3 θ + \frac{π}{3}) = - 1

3 θ + \frac{π}{3} = \frac{3 π}{4} + πn

Solve

3 θ + \frac{π}{3} = \frac{3 π}{4} + πn : θ = \frac{πn}{3} + \frac{5 π}{36}

θ = \frac{πn}{3} + \frac{5 π}{36}

3 sec^{2} (x) - 6 = 0, 0 \leq x \leq 2 π

cot^{2} (x) = 1

2 tan (x) - sec^{2} (x) = 0

4 sin^{2} (2 x) + 2 = 3

- \frac{1}{4} sin (\frac{x}{2}) = 0

What is the general solution for 5+2tan(3θ+pi/3)=3 ?
The general solution for 5+2tan(3θ+pi/3)=3 is θ=(pin)/3+(5pi)/(36)