1. ## Proving Trig Identities

I need help proving this Trig Identity:

sin2(x\2) = (tanx-sinx)/2tanx

Thanks.

2. ## Re: Proving Trig Identities

Simplify the right-hand side to (1 - cos(x))/2, then use the formula for cos(2 * x/2).

3. ## Re: Proving Trig Identities

Start with the right hand side. Wherever you see tanx replace it with sinx/cosx. Simplify what you get.
The use the identity cosx=1-2sin^2x/2

4. ## Re: Proving Trig Identities

I am afraid I don't know the identity cosx=1-2sin^2x/2.

5. ## Re: Proving Trig Identities

Do you know the identity cos2x=1-2sin^2x? This is true any time the angle on the left hand side is twice the angle on the right hand side. Hence the identity I quoted.

6. ## Re: Proving Trig Identities

Okay, I see the identity you quoted. I must have made a mistake somewhere in calculations. After rewriting tan x as sin x / cos x and simplifying I end up with (1-sin x) / 2.

7. ## Re: Proving Trig Identities

Originally Posted by biffboy
Do you know the identity cos2x=1-2sin^2x?
And if you are not sure, you should know the identity $\cos2x=\cos^2x-\sin^2x$, which together with $\cos^2x+\sin^2x=1$ gives $\cos2x=1-2\sin^2x$.

8. ## Re: Proving Trig Identities

Originally Posted by ostheimerdl
After rewriting tan x as sin x / cos x and simplifying I end up with (1-sin x) / 2.
$\frac{\sin x}{\tan x}=\frac{\sin x}{\frac{\sin x}{\cos x}}=\frac{\sin x\cdot \cos x}{\sin x}=\cos x$.

9. ## Re: Proving Trig Identities

You should have got (1-cosx)/2