# trigo idnentitis question

• Sep 4th 2008, 01:54 AM
sanikui
trigo idnentitis question
Prove the identity:
1. sin(A-B)cosB+cos (A-B)sinB=sinA
2. Prove that sin(∏/4 + A) - sin(∏/4 - A)=Square root 2 sinA
THANK YOU
• Sep 4th 2008, 03:24 AM
mr fantastic
Quote:

Originally Posted by sanikui
Prove the identity:
sin(A-B)cosB+cos (A-B)sinB=A
Prove that sin(∏/4 + A) - sin(∏/4 - A)=Square root 2 sinA

In both cases you should start by using the compound angle formulae:

sin(A - B) = sin A cos B - sin B cos A
cos(A - B) = cos A cos B + sin A sin B
sin(A + B) = sin A cos B + sin B cos A

I'm assuming there's something missing on the right hand side of the first one .......

For the second one it also helps to know that $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$.

Where are you stuck?
• Sep 4th 2008, 05:18 AM
sanikui
Sorry for write wrong...
That is sin(A-B)cosB+cos (A-B)sinB=sinA
(Rock)
• Sep 9th 2008, 06:01 AM
sanikui
Know do liaw
1.RHS=(sinAcosB-cosAsinB)cosB+(cosAcosB+sinAsinB)sinB
=sinAcos^2B+sinAsin^2B
=sinA(cos^2B+sin^2B)
=sinA(1)
=sinA

THX Mr Fantastic