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

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- Dec 12th 2011, 06:15 PMahmedbtrig 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 PMskeeterRe: trig proof help
start with the basic ratio identity for tangent ...

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

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

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

and cosine ...

$\displaystyle \cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1+\cos{x}}{2}}$ - Dec 12th 2011, 09:06 PMSironRe: trig proof help
You can also use the t-formulas.

Let$\displaystyle \tan\left(\frac{x}{2}\right)=t$ then

$\displaystyle \sin(x)=\frac{2t}{1+t^2}$

$\displaystyle \cos(x)=\frac{1-t^2}{1+t^2}$ - Dec 13th 2011, 05:37 AMahmedbRe: trig proof help
no i am not talking about this.

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 AMe^(i*pi)Re: trig proof help
Use the double angle identities to express sin and cos in terms of their half-angles since $\displaystyle \sin(x) = \sin \left[2\left(\frac{x}{2}\right)\right]$

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

$\displaystyle \dfrac{2\sin(\theta)\cos(\theta)}{1+2\cos^2 (\theta) -1} = \dfrac{2\sin \theta \cos \theta}{2\cos^2 \theta}$ - Dec 13th 2011, 05:50 AMahmedbRe: trig proof help
i still don't kind of get it

can you show the steps? - Dec 13th 2011, 07:32 AMahmedbRe: trig proof help
I still need help

- Dec 13th 2011, 07:45 AMPlatoRe: trig proof help
$\displaystyle \sin (x) = \sin \left( {2\cdot\tfrac{x}{2}} \right) = 2\sin \left( {\tfrac{x}{2}} \right)\cos \left( {\tfrac{x}{2}} \right)$.

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

Use those two in $\displaystyle \frac{\sin(x)}{\cos(x)+1}$ it falls right out. - Dec 13th 2011, 07:59 AMahmedbRe: trig proof help
so what do you do with the (+1)?

- Dec 13th 2011, 08:03 AMQuackyRe: trig proof help
Have you tried the suggested substitution in post #8? If you have, you'll soon see what happens to the +1.