What is the general solution for 2tan(2x)-6=0 ?

The general solution for 2tan(2x)-6=0 is x=(1.24904…)/2+(pin)/2

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2tan(2x)-6=0

2 tan (2 x) - 6 = 0

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

Degrees

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

Solution steps

2 tan (2 x) - 6 = 0

Move

6

to the right side

2 tan (2 x) - 6 = 0

Add

6

to both sides

2 tan (2 x) - 6 + 6 = 0 + 6

Simplify

2 tan (2 x) = 6

2 tan (2 x) = 6

Divide both sides by

2

2 tan (2 x) = 6

Divide both sides by

2

\frac{2 tan ( 2 x )}{2} = \frac{6}{2}

Simplify

tan (2 x) = 3

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}

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- 2 sin (x) = 1

- 5 sin (x) = - 2 cos^{2} (x) + 4, 0 \leq x \leq 2 π

6 = sin (\frac{π}{4} x) + 5

What is the general solution for 2tan(2x)-6=0 ?
The general solution for 2tan(2x)-6=0 is x=(1.24904…)/2+(pin)/2