I need help proving this Trig Identity:

sin^{2}(x\2) = (tanx-sinx)/2tanx

Thanks.

Printable View

- April 2nd 2012, 09:59 AMostheimerdlProving Trig Identities
I need help proving this Trig Identity:

sin^{2}(x\2) = (tanx-sinx)/2tanx

Thanks. - April 2nd 2012, 10:05 AMemakarovRe: Proving Trig Identities
Simplify the right-hand side to (1 - cos(x))/2, then use the formula for cos(2 * x/2).

- April 2nd 2012, 10:14 AMbiffboyRe: 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 - April 2nd 2012, 10:30 AMostheimerdlRe: Proving Trig Identities
I am afraid I don't know the identity cosx=1-2sin^2x/2.

- April 2nd 2012, 11:01 AMbiffboyRe: 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.

- April 2nd 2012, 11:22 AMostheimerdlRe: 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.

- April 2nd 2012, 11:25 AMemakarovRe: Proving Trig Identities
- April 2nd 2012, 11:29 AMemakarovRe: Proving Trig Identities
- April 2nd 2012, 11:40 AMbiffboyRe: Proving Trig Identities
You should have got (1-cosx)/2