# Thread: Integral Problem

1. ## Integral Problem

ok so i got this problem from and A level Past Paper, and i've been trying to solve it for quite a long time.. to no avail... i've got a feeling it's soooo easy, but nonetheless the answer just keeps eluding me... and the question goes something like this

Use the substitution t = tan(x) to find

∫(1/(cos(2x)-3(sin(x))^2))

I've been trying all sorts of trig identities.. still haven't managed to solve it xD

any help would be greatly appreciated

thank you

p.s. Sry about the layout xD

2. Originally Posted by XonBugeja
ok so i got this problem from and A level Past Paper, and i've been trying to solve it for quite a long time.. to no avail... i've got a feeling it's soooo easy, but nonetheless the answer just keeps eluding me... and the question goes something like this

Use the substitution t = tan(x) to find

∫(1/(cos(2x)-3(sin(x))^2))

I've been trying all sorts of trig identities.. still haven't managed to solve it xD

any help would be greatly appreciated

thank you

p.s. Sry about the layout xD
I'm guessing you're having trouble putting everything into tan x?

Fear not. Wikipedia has this excellent table which shows each trigonometric functions in terms of the other ones.

So
$\sin x = \frac{\tan x}{\sqrt{1+\tan ^2 x}}$

$\cos x = \frac{1}{\sqrt{1+\tan ^2 x}}$

Or you could also use:

$\cos (2x) = \frac{1- \tan ^2 x}{1+\tan ^2 x}$

3. :O this was a post paper question so i was only using the identities that i was given on the booklet they usually supply with the exam.. those were not there XD guess i'll have to learn them by heart lol

but ye they were the key i managed to work it out perfectly!

Many thanks ^.^