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

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- Sep 4th 2008, 01:54 AMsanikuitrigo 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 AMmr fantastic
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 $\displaystyle \sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$.

Where are you stuck? - Sep 4th 2008, 05:18 AMsanikui
Sorry for write wrong...

That is sin(A-B)cosB+cos (A-B)sinB=sinA

(Rock) - Sep 9th 2008, 06:01 AMsanikui
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