1. ## 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

2. 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?

3. Sorry for write wrong...
That is sin(A-B)cosB+cos (A-B)sinB=sinA

4. 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