# Thread: [SOLVED] Sum and difference identities

1. ## [SOLVED] Sum and difference identities

Q) if $sin \alpha =12/13 , \alpha$ is in the first quadrant ; $sin \beta =7/25 , \beta$ in the first quadrants.
Find a) $sin (\alpha+\beta)$ b) $cos(\alpha+\beta)$c)the quadrant containing $(\alpha +\beta)$
Thank you

2. $\sin\alpha$ = 12/13 gives
$\cos\alpha = sqrt{1 - (12/13)^2}$
=> $\sin\alpha = 5/13$

Similarly $\cos\beta = 24/25$

Now expand $\sin (\alpha + \beta)$ and $\cos(\alpha + \beta)$ in terms of $\sin\alpha, \cos\alpha$ and $\sin\beta, \cos\beta$
After this replace the value and proceed.

3. ## solve

the soluation..............

4. Hello ekledes
Your solution is all right, excpet for c part.
$\alpha + \beta$ is in first qurdrant, but niot because $0 < \sin(\alpha + \beta) < 1$, but because $0 < \cos(\alpha + \beta) < 1.$
Sine function is positive in both first and second quadrant. Its cos function which is negative in second quadrant. So here deciding factor is cos value not sin value

5. in deed iam choose this condition 0<sin(x+y)<1
becouse the function cos is belong to the same interval