# trig proof help

• Dec 12th 2011, 06:15 PM
ahmedb
trig proof help
sinx/(1+cosx)
simplify that so it equals:
tan(x/2)

(1-cosx)/sinx
simplify that so it equals:
tan(x/2)

so can someone post the steps please and thanks
• Dec 12th 2011, 06:26 PM
skeeter
Re: trig proof help
Quote:

Originally Posted by ahmedb
sinx/(1+cosx)
simplify that so it equals:
tan(x/2)

(1-cosx)/sinx
simplify that so it equals:
tan(x/2)

so can someone post the steps please and thanks

start with the basic ratio identity for tangent ...

$\tan\left(\frac{x}{2}\right) = \frac{\sin\left(\frac{x}{2}\right)}{\cos \left(\frac{x}{2}\right)}$

you will also need the half-angle identities for sine ...

$\sin\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos{x}}{2}}$

and cosine ...

$\cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1+\cos{x}}{2}}$
• Dec 12th 2011, 09:06 PM
Siron
Re: trig proof help
You can also use the t-formulas.
Let $\tan\left(\frac{x}{2}\right)=t$ then
$\sin(x)=\frac{2t}{1+t^2}$
$\cos(x)=\frac{1-t^2}{1+t^2}$
• Dec 13th 2011, 05:37 AM
ahmedb
Re: trig proof help
i am talking about,
sin(x)/(1+cos(x))

when you simplify that you get tan(x/2)
so how do you get tan(x/2) from the other equation?
• Dec 13th 2011, 05:42 AM
e^(i*pi)
Re: trig proof help
Quote:

Originally Posted by ahmedb
i am talking about,
sin(x)/(1+cos(x))

when you simplify that you get tan(x/2)
so how do you get tan(x/2) from the other equation?

Use the double angle identities to express sin and cos in terms of their half-angles since $\sin(x) = \sin \left[2\left(\frac{x}{2}\right)\right]$

Let $\theta = \dfrac{x}{2}$ and we arrive at:

$\dfrac{2\sin(\theta)\cos(\theta)}{1+2\cos^2 (\theta) -1} = \dfrac{2\sin \theta \cos \theta}{2\cos^2 \theta}$
• Dec 13th 2011, 05:50 AM
ahmedb
Re: trig proof help
i still don't kind of get it
can you show the steps?
• Dec 13th 2011, 07:32 AM
ahmedb
Re: trig proof help
I still need help
• Dec 13th 2011, 07:45 AM
Plato
Re: trig proof help
Quote:

Originally Posted by ahmedb
I still need help

$\sin (x) = \sin \left( {2\cdot\tfrac{x}{2}} \right) = 2\sin \left( {\tfrac{x}{2}} \right)\cos \left( {\tfrac{x}{2}} \right)$.

In a similar way we get $\cos (x) = \cos \left( {2\cdot\tfrac{x}{2}} \right) = 2\cos^2 \left( {\tfrac{x}{2}} \right)-1$.

Use those two in $\frac{\sin(x)}{\cos(x)+1}$ it falls right out.
• Dec 13th 2011, 07:59 AM
ahmedb
Re: trig proof help
so what do you do with the (+1)?
• Dec 13th 2011, 08:03 AM
Quacky
Re: trig proof help
Have you tried the suggested substitution in post #8? If you have, you'll soon see what happens to the +1.