What is the general solution for tan(3x)*tan(30)=1 ?

The general solution for tan(3x)*tan(30)=1 is x=20+(180n)/3

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tan(3x)*tan(30)=1

tan (3 x) \cdot tan (3 0^{\circ}) = 1

x = 2 0^{\circ} + \frac{18 0 ^{\circ} n}{3}

Solution steps

tan (3 x) tan (3 0^{\circ}) = 1

tan (3 0^{\circ}) = \frac{3}{3}

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

Multiply both sides by

3

3 tan (3 x) = 3

Divide both sides by

3

tan (3 x) = 3

General solutions for

tan (3 x) = 3

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

Solve

3 x = 6 0^{\circ} + 18 0^{\circ} n : x = 2 0^{\circ} + \frac{18 0 ^{\circ} n}{3}

x = 2 0^{\circ} + \frac{18 0 ^{\circ} n}{3}

3 - 6 sin (2 x) = 0

\frac{1}{1} + cot^{2} (x) = sin^{2} (x)

x, 2 cos (x) = 2 cos (3 x)

sin (x) = 1 - 2 sin^{2} (x)

2 sin^{2} (t) - cos (t) - 1 = 0

What is the general solution for tan(3x)*tan(30)=1 ?
The general solution for tan(3x)*tan(30)=1 is x=20+(180n)/3