What is the general solution for 2tan(2x)=-4sqrt(2) ?

The general solution for 2tan(2x)=-4sqrt(2) is x=-(1.23095…)/2+(pin)/2

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2tan(2x)=-4sqrt(2)

2 tan (2 x) = - 42

x = - \frac{1.23095 \dots}{2} + \frac{πn}{2}

Degrees

x = - 35.26438 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 tan (2 x) = - 42

Divide both sides by

2

2 tan (2 x) = - 42

Divide both sides by

2

\frac{2 tan ( 2 x )}{2} = \frac{- 4 2}{2}

Simplify

\frac{2 tan ( 2 x )}{2} = \frac{- 4 2}{2}

Simplify

\frac{2 tan ( 2 x )}{2} : tan (2 x)

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

Divide the numbers:

\frac{2}{2} = 1

= tan (2 x)

Simplify

\frac{- 4 2}{2} : - 22

\frac{- 4 2}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 2}{2}

Divide the numbers:

\frac{4}{2} = 2

= - 22

tan (2 x) = - 22

tan (2 x) = - 22

tan (2 x) = - 22

Apply trig inverse properties

tan (2 x) = - 22

General solutions for

tan (2 x) = - 22

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

2 x = arctan (- 22) + πn

2 x = arctan (- 22) + πn

Solve

2 x = arctan (- 22) + πn : x = - \frac{arctan ( 2 2 )}{2} + \frac{πn}{2}

2 x = arctan (- 22) + πn

Simplify

arctan (- 22) + πn : - arctan (22) + πn

arctan (- 22) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 22) = - arctan (22)

= - arctan (22) + πn

2 x = - arctan (22) + πn

Divide both sides by

2

2 x = - arctan (22) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{1.23095 \dots}{2} + \frac{πn}{2}

(4 sin (x) + 1) (2 sin (x) + 1) = 0

2 sin (3 x) \cdot sin (x) = 1

(\frac{2}{2}) (cos (θ) + sin (θ)) = 1

arcsin (6 x) + arcsin (6 3 x) = - \frac{π}{2}

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

What is the general solution for 2tan(2x)=-4sqrt(2) ?
The general solution for 2tan(2x)=-4sqrt(2) is x=-(1.23095…)/2+(pin)/2