# Solve the following problem in terms of tan(x):

• Nov 23rd 2006, 08:21 PM
qbkr21
Solve the following problem in terms of tan(x):
Guys I need some help getting $\displaystyle Tan(x)$ by itself could you please help?

$\displaystyle \frac{3}{\sqrt7}$=$\displaystyle \frac{2*tan(x)}{1-(tan(x))^2}$

Thanks so much for the help I am looking forward to seeing how you work it out.
• Nov 23rd 2006, 09:09 PM
malaygoel
Quote:

Originally Posted by qbkr21
Guys I need some help getting $\displaystyle Tan(x)$ by itself could you please help?

$\displaystyle \frac{3}{\sqrt7}$=$\displaystyle \frac{2*tan(x)}{1-(tan(x))^2}$

Thanks so much for the help I am looking forward to seeing how you work it out.

for the sake of calculation,we replace tanx by y
$\displaystyle \frac{3}{\sqrt7}$=$\displaystyle \frac{2y}{1-y^2}$
$\displaystyle 3(1-y^2)$=$\displaystyle 2y*\sqrt{7}$
$\displaystyle 3-3y^2$=$\displaystyle 2y*\sqrt{7}$
$\displaystyle 3y^2+2\sqrt{7}y-3=$
$\displaystyle y=\frac{-2\sqrt{7}+8}{6}$ or $\displaystyle y=\frac{-2\sqrt{7}-8}{6}$
i.e.
$\displaystyle tanx=\frac{-2\sqrt{7}+8}{6}$ or $\displaystyle tanx=\frac{-2\sqrt{7}-8}{6}$
equivalently
$\displaystyle tanx=\frac{-\sqrt{7}+4}{3}$ or $\displaystyle tanx=\frac{-\sqrt{7}-4}{3}$

Keep Smiling
Malay
• Nov 23rd 2006, 09:43 PM
qbkr21
Re:
So really what I need to do to is just cross multiply...
• Nov 23rd 2006, 09:56 PM
malaygoel
Quote:

Originally Posted by qbkr21
So really what I need to do to is just cross multiply...

actually what you have to do is to form a equation with tanx using given condition
in this question, for the above purpose, first you have to cross multiply and then rearrange st that a standard quadratic equation is before you.

Keep Smiling
Malay
• Nov 23rd 2006, 10:15 PM
qbkr21
Re:
This sounds like a dreadful problem to solve, long & befuddling?

$\displaystyle \text{{"Curiosity has its own reason for existence?"}}$
• Nov 23rd 2006, 10:24 PM
malaygoel
Quote:

Originally Posted by qbkr21
This sounds like a dreadful problem to solve, long & befuddling?

$\displaystyle \text{{"Curiosity has its own reason for existence?"}}$

if you know certain basic things, you just have to apply it
question is not long, this is here to show you that why you studied crooss multiplying in lower classes, reaarangement a little later and solution of quadratic equations.
Now, this is a quetion given for practice which may or may not have practical value, when you study undergraduate courses, you have to apply your basic concepts like these to solve real life problems(you may have heard of boeing 747, here 747 is derived from sin45=.747 since it was used very frequently is degining the plane)

Keep Smiling
Malay