Proof Problem of Condition Trigonometrical Identities

[anurag]

Hello,

I was doing some random problems of Trigonometry and I came across a rather difficult problem for me at least (I study in grade 10)
It is a problem of conditional trigonometrical identities. BTW this may be very easy and I might just have been too dumb. Anyways, I would love some help. The problem goes like this:

* IF A+B+C = 2S, Prove that :

sin S sin (S-A)+sin (S-B) sin (S-C) = sin B sin C

Thank you for the kind cooperation
- Anurag

 

[Ishuda]

Hello,

I was doing some random problems of Trigonometry and I came across a rather difficult problem for me at least (I study in grade 10)
It is a problem of conditional trigonometrical identities. BTW this may be very easy and I might just have been too dumb. Anyways, I would love some help. The problem goes like this:

* IF A+B+C = 2S, Prove that :

sin S sin (S-A)+sin (S-B) sin (S-C) = sin B sin C

Thank you for the kind cooperation
- Anurag

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


Hint: To repeat with labeled equations we have
Prove that if
(1) A+B+C = 2S
then
(2) sin S sin (S-A)+sin (S-B) sin (S-C) = sin B sin C

Well since A doesn't appear on the right hand side of (2), I would start by using (1) to substitute for S-A on the left hand side of (2). Then start using the sum and difference equations for trig functions, i.e.
sin(a\(\displaystyle \pm\)b)=sin(a)cos(b)\(\displaystyle \pm\)sin(b)cos(a)
and so forth. Of course other substitutions are available so, you pays your money and takes your choice.

 

[anurag]

Proved

THanks for the help