# Proving Trig Identities

• Apr 2nd 2012, 08:59 AM
ostheimerdl
Proving Trig Identities
I need help proving this Trig Identity:

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

Thanks.
• Apr 2nd 2012, 09:05 AM
emakarov
Re: Proving Trig Identities
Simplify the right-hand side to (1 - cos(x))/2, then use the formula for cos(2 * x/2).
• Apr 2nd 2012, 09:14 AM
biffboy
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
• Apr 2nd 2012, 09:30 AM
ostheimerdl
Re: Proving Trig Identities
I am afraid I don't know the identity cosx=1-2sin^2x/2.
• Apr 2nd 2012, 10:01 AM
biffboy
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.
• Apr 2nd 2012, 10:22 AM
ostheimerdl
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.
• Apr 2nd 2012, 10:25 AM
emakarov
Re: Proving Trig Identities
Quote:

Originally Posted by biffboy
Do you know the identity cos2x=1-2sin^2x?

And if you are not sure, you should know the identity $\displaystyle \cos2x=\cos^2x-\sin^2x$, which together with $\displaystyle \cos^2x+\sin^2x=1$ gives $\displaystyle \cos2x=1-2\sin^2x$.
• Apr 2nd 2012, 10:29 AM
emakarov
Re: Proving Trig Identities
Quote:

Originally Posted by ostheimerdl
After rewriting tan x as sin x / cos x and simplifying I end up with (1-sin x) / 2.

$\displaystyle \frac{\sin x}{\tan x}=\frac{\sin x}{\frac{\sin x}{\cos x}}=\frac{\sin x\cdot \cos x}{\sin x}=\cos x$.
• Apr 2nd 2012, 10:40 AM
biffboy
Re: Proving Trig Identities
You should have got (1-cosx)/2