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

The general solution for tan(2x)=3 is x=(1.24904…)/2+(pin)/2

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tan(2x)=3

tan (2 x) = 3

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

Degrees

x = 35.78252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = 3

Apply trig inverse properties

tan (2 x) = 3

General solutions for

tan (2 x) = 3

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x = arctan (3) + πn

2 x = arctan (3) + πn

Solve

2 x = arctan (3) + πn : x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

2 x = arctan (3) + πn

Divide both sides by

2

2 x = arctan (3) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

3 = tan (x)

sin (x) tan (x) = 3 sin (x)

12 tan (θ) + 5 = 5 tan (θ) + 5

1 - sin (x) - 2 sin^{2} (x) = 0

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

What is the general solution for tan(2x)=3 ?
The general solution for tan(2x)=3 is x=(1.24904…)/2+(pin)/2