1. ## 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

2. ## Re: trig proof help

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

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

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 ...

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

3. ## Re: trig proof help

You can also use the t-formulas.
Let$\displaystyle \tan\left(\frac{x}{2}\right)=t$ then
$\displaystyle \sin(x)=\frac{2t}{1+t^2}$
$\displaystyle \cos(x)=\frac{1-t^2}{1+t^2}$

4. ## Re: trig proof help

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?

5. ## Re: trig proof help

Originally Posted by ahmedb
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 $\displaystyle \sin(x) = \sin \left[2\left(\frac{x}{2}\right)\right]$

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

$\displaystyle \dfrac{2\sin(\theta)\cos(\theta)}{1+2\cos^2 (\theta) -1} = \dfrac{2\sin \theta \cos \theta}{2\cos^2 \theta}$

6. ## Re: trig proof help

i still don't kind of get it
can you show the steps?

7. ## Re: trig proof help

I still need help

8. ## Re: trig proof help

Originally Posted by ahmedb
I still need 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.

9. ## Re: trig proof help

so what do you do with the (+1)?

10. ## 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.