Q. Prove that- Sin(A+B)=SinA.CosB + CosA.SinB using this SPECIFIC figure.

[utkarshmttl]

Respected Members,
I hope this e-mail finds you in the best of your spirits.
If you'd be so kind as to help me, I'd like to discuss a question about Trigonometry with you which I am posting below. I'd really appreciate your help.

Q. Prove that-
Sin(A+B)=SinA.CosB + CosA.SinB
using the figure given below.

I have attached the given figure.


I have been able to prove the aforementioned identity using other geometries and also by using the concept of Complex numbers (Euler's theorem) but despite of pondering over this particular figure for hours at a time since months, I have only reached so far but nowhere near proving this identity.

I will await your reply and would be highly obliged.
Thank you.


Greetings,


--
UTKARSH
MITTAL

 

[stapel]

Is there any way to relate the method shown here and here to your graphic?

 

[utkarshmttl]

Is there any way to relate the method shown here and here to your graphic?

The figures used in the link you provided are the most commonly used ones to prove this identity, that is what makes this question tricky. I have tried relating this method and the unit radius circle method, but without any luck.

 

[utkarshmttl]

Well, in case this helps:
triangle PQR is similar to triangle PST (but I'm sure you knew that...)

If an example with all integer sides helps, here's one:
PS = 35, QS = 45, PT = 28, RT = 72, RQ = 60, TS = 21, RS = 75

Good luck!

You were right, I did know that but thanks a lot. Atleast there are people trying to help.