What is the general solution for 2tan(2x)-10=3.4641 ?

The general solution for 2tan(2x)-10=3.4641 is x=(1.42333…)/2+(pin)/2

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2tan(2x)-10=3.4641

2 tan (2 x) - 10 = 3.4641

x = \frac{1.42333 \dots}{2} + \frac{πn}{2}

Degrees

x = 40.77544 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 tan (2 x) - 10 = 3.4641

Move

10

to the right side

2 tan (2 x) - 10 = 3.4641

Add

10

to both sides

2 tan (2 x) - 10 + 10 = 3.4641 + 10

Simplify

2 tan (2 x) = 13.4641

2 tan (2 x) = 13.4641

Divide both sides by

2

2 tan (2 x) = 13.4641

Divide both sides by

2

\frac{2 tan ( 2 x )}{2} = \frac{13.4641}{2}

Simplify

tan (2 x) = \frac{13.4641}{2}

tan (2 x) = \frac{13.4641}{2}

Apply trig inverse properties

tan (2 x) = \frac{13.4641}{2}

General solutions for

tan (2 x) = \frac{13.4641}{2}

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

2 x = arctan (\frac{13.4641}{2}) + πn

2 x = arctan (\frac{13.4641}{2}) + πn

Solve

2 x = arctan (\frac{13.4641}{2}) + πn : x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{13.4641}{2}) + πn

Divide both sides by

2

2 x = arctan (\frac{13.4641}{2}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{13.4641}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.42333 \dots}{2} + \frac{πn}{2}

What is the general solution for 2tan(2x)-10=3.4641 ?
The general solution for 2tan(2x)-10=3.4641 is x=(1.42333…)/2+(pin)/2