Trig Identities

**Universe** · January 23rd 2008, 01:10 PM

Hi,
I have my math exam in a few days and that's the last question I have to solve to complete the trig part.
$2sin x(1+cos x) = \frac {2sin^3 x} {1-cos x}$
I've been trying to use sin^2x + cos^2x for LS and RS however I'm getting nowhere with that, mainly because of the right side fraction.
Any help appreciated.
Thank you very much!

**Krizalid** · January 23rd 2008, 01:31 PM

$2\sin x(1 + \cos x) = 2\sin x(1 + \cos x) \cdot \frac{{1 - \cos x}}<br /> {{1 - \cos x}} = \frac{{2\sin x\left( {1 - \cos ^2 x} \right)}}<br /> {{1 - \cos x}}.$

The rest follows.

**Universe** · January 23rd 2008, 01:36 PM

I see...
So you are allowed to multiply 1-cos x over 1-cos x at any time?
I mean if I'd get anything similar in my exam I can just multiply it like that?
Thanks

**Krizalid** · January 23rd 2008, 01:41 PM

Originally Posted by Universe

I see...
So you are allowed to multiply 1-cos x over 1-cos x at any time?

It's like multiplyin' by 1. It's like $\frac aa.$

Originally Posted by Universe

I mean if I'd get anything similar in my exam I can just multiply it like that?

That depends of the problem.

For example your trig. identity could've been tackled by workin' the RHS.

**galactus** · January 23rd 2008, 01:43 PM

Work with the right side and show it equals the left side.

Multiply top and bottom of right side by $1+cos(x)$

$\frac{2sin^{3}(x)}{1-cos(x)}\cdot\frac{1+cos(x)}{1+cos(x)}$

$=\frac{2sin^{3}(x)+2sin^{3}(x)cos(x)}{sin^{2}(x)}$

$2sin(x)+2sin(x)cos(x)$

Factor:

$2sin(x)(1+cos(x))$

**Universe** · January 23rd 2008, 01:51 PM

Alright.
Thank you very much guys.

Thread: Trig Identities

LinkBack

Thread Tools

Display

Trig Identities

Similar Math Help Forum Discussions

Trig Identities

Trig identities

Trig Identities

Trig Identities

Trig Identities Help!!!!

Search Tags