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

The general solution for tan(2x)=-2 is x=-(1.10714…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(2x)=-2

tan (2 x) = - 2

x = - \frac{1.10714 \dots}{2} + \frac{πn}{2}

Degrees

x = - 31.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = - 2

Apply trig inverse properties

tan (2 x) = - 2

General solutions for

tan (2 x) = - 2

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

2 x = arctan (- 2) + πn

2 x = arctan (- 2) + πn

Solve

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

2 x = arctan (- 2) + πn

Simplify

arctan (- 2) + πn : - arctan (2) + πn

arctan (- 2) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 2) = - arctan (2)

= - arctan (2) + πn

2 x = - arctan (2) + πn

Divide both sides by

2

2 x = - arctan (2) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{1.10714 \dots}{2} + \frac{πn}{2}

tan^{3} (x) - 1 tan (x) = 0

2 cos (x) - 1 = 0, 0 \leq x \leq 2 π

tan (2 x) = 2

sin (2 x) = cos (2 x) + 1

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

What is the general solution for tan(2x)=-2 ?
The general solution for tan(2x)=-2 is x=-(1.10714…)/2+(pin)/2