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

The general solution for tan(x/2-pi/2)=sqrt(2) is x=2*0.95531…+2pin+pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x/2-pi/2)=sqrt(2)

tan (\frac{x}{2} - \frac{π}{2}) = 2

x = 2 \cdot 0.95531 \dots + 2 πn + π

Degrees

x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{x}{2} - \frac{π}{2}) = 2

Apply trig inverse properties

tan (\frac{x}{2} - \frac{π}{2}) = 2

General solutions for

tan (\frac{x}{2} - \frac{π}{2}) = 2

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

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

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

Solve

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

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

Move

\frac{π}{2}

to the right side

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

Add

\frac{π}{2}

to both sides

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

Simplify

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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2} : 2 arctan (2) + 2 πn + π

2 arctan (2) + 2 πn + 2 \cdot \frac{π}{2}

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{2}

Cancel the common factor:

2

= π

= 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

Show solutions in decimal form

x = 2 \cdot 0.95531 \dots + 2 πn + π

8 sec (x) + 8 tan (x) = 8

25 cot^{2} (θ) - 16 = 0

2 sin^{2} (x) = sin (x) + 1

sin (3 x) = - \frac{3}{2}

3 sin (2 x) sin (x) = 3 cos (x)

What is the general solution for tan(x/2-pi/2)=sqrt(2) ?
The general solution for tan(x/2-pi/2)=sqrt(2) is x=2*0.95531…+2pin+pi