calculus trig integral problem

Question

anonymous · Answer

$$\int\limits \frac{ 1 }{ \cos \theta - 1 }d \theta $$

anonymous · Answer

I'm not quite sure how to approach this problem

anonymous · Answer

u-substitution won't work and integration by parts doesn't seem like a good idea here either, it is not in inverse trig form, and i dont think partial fractions could apply either

mathmale · Answer

Try using an identity to simplify the denominator.  What is the conjugate of cos theta - 1 ?

anonymous · Answer

cos theta + 1

anonymous · Answer

i started doing that but it didnt seem to be going anywhere

mathmale · Answer

Try multiplying both numerator and den. of the given fraction by that.

anonymous · Answer

yeah cos theta +1 / cos^2 theta -1

anonymous · Answer

i could split it into two fractions but then what?

mathmale · Answer

Let's be careful to eliminate any confusion:  please put parentheses around your denominator.

anonymous · Answer

cos theta - 1 / (cos^2 theta - 1)

mathmale · Answer

What is (cos theta)^2 - 1 equal to?

anonymous · Answer

sorry i meant plus at the top

anonymous · Answer

it equals (-sin^2 theta)

mathmale · Answer

Use a relevant trig identity.

mathmale · Answer

Now, what happens if you separate your whole expression into two expressions?

anonymous · Answer

do you mean like a power reduction formula when you say relevant?

mathmale · Answer

no...think "substitution"

anonymous · Answer

when you split it then it would be ((cos theta) / (cos^2 theta -1))  - (1 / (cos^2 theta -1 )

mathmale · Answer

Can you integrate |dw:1449022749606:dw|