Help with Limit: ((sin a)(sin 2a))/(1- cos a) as 'a approaches 0

[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

 

[Aftermarth]

well we can't 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 :)

 

[g_edgar]

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

 

[Bohrok]

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.

 

[Mark44]

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.

What "they" say about this limit is correct.

 

[charliemagne]

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.

What "they" say about this limit is correct.

thank you

I got it

thank you for the 'hint'