Proving the Half-Angle Formula for Tangent Using Trigonometric Identities

[xonicole]

Homework Statement

tanx/2 = (1-cosx)/sinx

Homework Equations

The Attempt at a Solution

This is where i got on the right side
i don't know where to finish...(1-cosx)/sinx

 

[Gib Z]

Well, are you familiar with Weierstrass substitution? They are also known as t-formula:
http://pear.math.pitt.edu/Calculus2/week3/3_2li5.html

Another method would be to use the Double angle identities:
$$\cos (2\theta) = 1- 2\sin^2 \theta$$ and $$\sin (2\theta) = 2 \sin \theta \cos \theta$$.

Into those, let $\theta = x/2$, and put those back into what you have and simplify.

 

[xonicole]

I found that a lot of people have been telling me that but i don't understand how you use that to make the sides equal is there a way you can show me step by step

 

[Gib Z]

No really I can't ! You didn't even tell me which of the two methods I posted you want help with. Show us what you have tried to do yourself, so we can help you get over what you're stuck with.