SOLUTION: Would be ever so much grateful for help to prove the trigonometric relation in a thoroughly detailed explanation of proof.
{{{tan (x/2)= (1-cosx)/ (sinx)}}}
Question 667155: Would be ever so much grateful for help to prove the trigonometric relation in a thoroughly detailed explanation of proof. Found 2 solutions by tam144, Edwin McCravy:Answer by tam144(6) (Show Source): You can put this solution on YOUR website! Start from the right side of the equation. Refer to List of Trig Identities
in book titled:"Solving trig equations and inequalities" (Amazon e-book 2010)
1 - cos x = 2 sin^2 x/2 (Identity 11B)
sin x = 2sin x/2.cos x/2 (Identity 10)
Quotient: (1 - cos x)/sin x = (2sin^2 x/2)/(2sin x/2.cos/x/2)
After simplification, the quotient becomes:
!1 - cos x)/sin x = (sin x/2) / (cos x/2) = tg x/2 Answer by Edwin McCravy(20064) (Show Source): You can put this solution on YOUR website!
Let =
which means =
Then the identity becomes
=
We will work with the right side:
Use the identities and
=
=
Use the identity in the numerator
=
=
=
=
Use the identity
=
Substitute for
=
Edwin