Could anyone give me some hints? I can't think the first step~

Given that $\displaystyle \sin x + \ sin y = a$,

$\displaystyle \cos x + \ cos y = b$,

express the following in therms of a and b:

(a) cos (x - y)

(b) sin (x - y)

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- Apr 17th 2006, 07:27 AMling_c_0202express cos (x - y)
Could anyone give me some hints? I can't think the first step~

Given that $\displaystyle \sin x + \ sin y = a$,

$\displaystyle \cos x + \ cos y = b$,

express the following in therms of a and b:

(a) cos (x - y)

(b) sin (x - y) - Apr 17th 2006, 07:50 AMThePerfectHackerQuote:

Originally Posted by**ling_c_0202**

$\displaystyle a=\sin x+\sin y$

Thus,

$\displaystyle a^2=\sin^2x+\sin^2y+2\sin x\sin y$

Thus,

$\displaystyle b^2=\cos^2x+\cos^2y+2\cos x\cos y$

Thus,

$\displaystyle a^2+b^2=\sin^2x+\cos^2x+\sin^2y+$$\displaystyle \cos^2y+2\sin x\sin y+2\cos x\cos y$

Thus,

$\displaystyle a^2+b^2=1+1+2(\cos x\cos y+\sin x\sin y)$

Thus,

$\displaystyle \frac{a^2+b^2}{2}-1=\cos(x-y)$ - Apr 17th 2006, 07:58 AMrgep
Try multiplying each relation by $\displaystyle \sqrt{\frac12}$ and adding and subtracting.

- Apr 18th 2006, 08:16 AMling_c_0202
Thank you very much!! ^^