What is the general solution for tan(pi/2-x)+2tan(pi/2+x)=1 ?

The general solution for tan(pi/2-x)+2tan(pi/2+x)=1 is x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(pi/2-x)+2tan(pi/2+x)=1

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

x = \frac{3 π}{4} + πn

Solution steps

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

Rewrite using trig identities

- \frac{cos ( x )}{sin ( x )} = 1

Subtract

1

from both sides

- \frac{cos ( x )}{sin ( x )} - 1 = 0

Simplify

- \frac{cos ( x )}{sin ( x )} - 1 : \frac{- cos ( x ) - sin ( x )}{sin ( x )}

\frac{- cos ( x ) - sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (x) - sin (x) = 0

Rewrite using trig identities

- 1 - tan (x) = 0

Move

1

to the right side

- tan (x) = 1

Divide both sides by

- 1

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

\frac{11.0994}{cos ( x )} = \frac{3.5355}{sin ( x )}

(\frac{sec ( x )}{cos ( x )})^{2} = tan^{2} (x)

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}

What is the general solution for tan(pi/2-x)+2tan(pi/2+x)=1 ?
The general solution for tan(pi/2-x)+2tan(pi/2+x)=1 is x=(3pi)/4+pin