Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

There is this trig equation:

$$ 5\tan x - 2\tan 2x = 0 \text{ for 0 < 0 < 360 } $$

So far I've gotten $$\tan x = \text{0, 180}$$ and all I have to solve now is $$\tan ^2x = 0.2$$ which gives me two angle, $24.1$ and $-24.1$. For some reason, this is wrong? Can someone please tell me where I'm going wrong? Thank you in advance!

UPDATE I'm so sorry! I made a mistake in my mathjax, I fixed it.

share|improve this question
1  
Hint : \begin{align} 5\tan x - 2\tan ^2x &= 0\\ (5 - 2\tan x)\tan x&=0\\ \tan x=0\qquad&;\qquad5 - 2\tan x=0 \end{align} –  Tunk-Fey Jul 27 at 12:38
    
@Shabbeh I made a mistake in my mathjax, so sorry! I fixed it though –  Samir Chahine Jul 27 at 12:43
    
It should be $\tan x = 2.5$ –  Darth Geek Jul 27 at 12:43

2 Answers 2

up vote 2 down vote accepted

Answer of the Original Version:

We have$$\tan x(2\tan x-5)=0$$

If $\tan x=0, x=n180^\circ$ where $n$ is any integer

If $\displaystyle2\tan x-5=0,\tan x=\frac52$

Google says $\displaystyle\arctan\frac52\approx68.1985905^\circ$

$\displaystyle\implies x\approx m180^\circ+68.1985905^\circ$ where $m$ is any integer

Probably you have meant $0<x<360^\circ\implies 0<m180^\circ+68.1985905^\circ<360^\circ$


Answer to the Edited Version:

Using Double Angle formula,

$$5\tan x=2\tan2x=2\frac{2\tan x}{1-\tan^2x}$$

$$\tan x(1-5\tan^2 x)=0$$

If $\tan x=0$ has been dealt already

$\displaystyle1-5\tan^2x=0\iff \tan^2x=\frac15\implies\cos2x=\frac{1-\tan^2x}{1+\tan^2x}=\frac23$

Using Google, $\displaystyle1\arccos\frac23\approx48.1896851$

$\displaystyle\implies2x=2m\pi\pm48.1896851^\circ\implies x=?$

Find $m$ such that $0<x<360^\circ$

share|improve this answer
    
I'm sorry I made a mistake while writing out my question, I had a different question, sorry. –  Samir Chahine Jul 27 at 12:43
    
@SamirChahine, Please find the edited version –  lab bhattacharjee Jul 27 at 12:58

Answered to original questions:

$$5\tan x - 2\tan^2 x = 0 \iff \tan x(5 - 2\tan x) = 0$$

Than means $5\tan x = 0\iff \tan x = 0\;$ or $\;2\tan x = 5 \iff \tan x = \frac 52$.

Can you take it from here?


share|improve this answer
1  
Rectify the sign –  lab bhattacharjee Jul 27 at 12:42
    
I had an error while writing my question, sorry! I fixed my question but I'm sure this would have been correct otherwise. –  Samir Chahine Jul 27 at 12:44
    
@amWhy Why have you removed the "you" from "can you take it from here?"? –  alexqwx Jul 27 at 12:56
1  
@alexqwx I thought 'you', I just forgot to write "you"! Thanks for pointing out the missing word! –  amWhy Jul 27 at 12:57

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.