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

**qbkr21** · November 23rd 2006, 08:21 PM

Guys I need some help getting $Tan(x)$ by itself could you please help?

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

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

**malaygoel** · November 23rd 2006, 09:09 PM

Originally Posted by qbkr21

Guys I need some help getting $Tan(x)$ by itself could you please help?

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

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
$\frac{3}{\sqrt7}$ = $\frac{2y}{1-y^2}$
$3(1-y^2)$ = $2y*\sqrt{7}$
$3-3y^2$ = $2y*\sqrt{7}$
$3y^2+2\sqrt{7}y-3=$
Applying quadratic formula
$y=\frac{-2\sqrt{7}+8}{6}$ or $y=\frac{-2\sqrt{7}-8}{6}$
i.e.
$tanx=\frac{-2\sqrt{7}+8}{6}$ or $tanx=\frac{-2\sqrt{7}-8}{6}$
equivalently
$tanx=\frac{-\sqrt{7}+4}{3}$ or $tanx=\frac{-\sqrt{7}-4}{3}$

Keep Smiling
Malay

**qbkr21** · November 23rd 2006, 09:43 PM

So really what I need to do to is just cross multiply...

**malaygoel** · November 23rd 2006, 09:56 PM

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

**qbkr21** · November 23rd 2006, 10:15 PM

This sounds like a dreadful problem to solve, long & befuddling?

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

**malaygoel** · November 23rd 2006, 10:24 PM

Originally Posted by qbkr21

This sounds like a dreadful problem to solve, long & befuddling?

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

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

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