1. ## Proving Question(Factor Formulae)

Prove $
(sinA+sinB)(sinA-sinB)=sin(A+B)sin(A-B)
$

2. Originally Posted by Punch
Prove $
(sinA+sinB)(sinA-sinB)=sin(A+B)sin(A-B)
$

3. Using factor formulae, $(sinA+sinB)(sinA-sinB)=2(sin(\frac{A+B}{2})cos(\frac{A-B}{2}))(2cos(\frac{A+B}{2})sin(\frac{A-B}{2}))$

stucked...

4. Anyone care to tell me if I am on the right track and how to go on?

5. Originally Posted by Punch
Anyone care to tell me if I am on the right track and how to go on?
Help required

6. Hello, Punch!

Prove: . $(\sin A+\sin B)(\sin A-\sin B)\:=\:\sin(A+B)\sin(A-B)$

$\sin(A\;+\;B)\sin(A\;-\;B) \;=\;\bigg[\sin A\cos B\;+\;\cos A\sin B\bigg]\,\bigg[\sin A\cos B\;-\;\cos A\sin B\bigg]$

. - - . . . . . . . . . . . $=\; \sin^2\!A\cos^2\!B \;\;-\;\; \cos^2\!A\sin^2\!B$

. . . . . . . . . . . $= \; \sin^2\!A\overbrace{(1-\sin^2\!B)} - \overbrace{(1-\sin^2\!A)}\sin^2\!B$

. . . . . . . . . . $=\; \sin^2\!A - \sin^2\!A\sin^2\!B - \sin^2\!B + \sin^2\!A\sin^2\!B$

. . . . . . . . . . . . . . . . . . $= \;\sin^2\!A - \sin^2\!B$

. . . . . . . . . . . . . . $= \;(\sin A + \sin B)\,(\sin A - \sin B)$

7. Originally Posted by Soroban
Hello, Punch!

$\sin(A\;+\;B)\sin(A\;-\;B) \;=\;\bigg[\sin A\cos B\;+\;\cos A\sin B\bigg]\,\bigg[\sin A\cos B\;-\;\cos A\sin B\bigg]$

. - - . . . . . . . . . . . $=\; \sin^2\!A\cos^2\!B \;\;-\;\; \cos^2\!A\sin^2\!B$

. . . . . . . . . . . $= \; \sin^2\!A\overbrace{(1-\sin^2\!B)} - \overbrace{(1-\sin^2\!A)}\sin^2\!B$

. . . . . . . . . . $=\; \sin^2\!A - \sin^2\!A\sin^2\!B - \sin^2\!B + \sin^2\!A\sin^2\!B$

. . . . . . . . . . . . . . . . . . $= \;\sin^2\!A - \sin^2\!B$

. . . . . . . . . . . . . . $= \;(\sin A + \sin B)\,(\sin A - \sin B)$
Thanks! You are a great help! Can I solve it using factor formulae?

How do I get as pro as you in trigonometry?

8. Originally Posted by Punch
How do I get as pro as you in trigonometry?
Want three words that will help you get to be a pro at mathematics?

Practice practice practice.

It's no good just reading a book on the subject, once you have done that get as many practice questions in as you can. It's the same with all topics in maths, some you might get straight way, others take a lot of work.

Also don't worry about getting stuck, getting stuck is how you learn things Look through past examples see if they're any use to you, if not there's this wonderful forum filled with extremely intelligent people that you can post your questions on