# Help with Limits

1. Jul 31, 2009

### charliemagne

Can someone answer this problem for me? please!

What is the limit of ((sin a)(sin 2a))/(1- cos a) as 'a approaches 0.'

they say the answer is 4.

I really don't get it.

thank you

P.S.: Is sin a + cos a = 1

Last edited: Jul 31, 2009
2. Jul 31, 2009

### Aftermarth

Re: limits

well we cant solve it for you but you have to think of limits like this (from what i remember)

sub in 0 and see what you get, and i think you will find its undefined at zero, so then you need to think what the curve is doing as it approaches zero. Put small numbers in and see where it is going :)

3. Jul 31, 2009

### g_edgar

Re: limits

One way to do it would use Tayor's Theorem.

4. Jul 31, 2009

### Bohrok

Re: limits

You want to somehow cancel out the 1-cosx in the denominator. sin a + cos a = 1 isn't the right identity but it's close, and that's one you'll need as well as the one with sin2a. Once you cancel 1-cosx, you can let a=0.

5. Jul 31, 2009

### Staff: Mentor

Re: limits

Rewrite sin 2a using the double angle identity.
Multiply numerator and denominator by 1 + cos a. That will get you 1 - cos2 a in the denominator.

6. Jul 31, 2009

### charliemagne

Re: limits

thank you

I got it

thank you for the 'hint'