# Thread: Find the value

1. ## Find the value

If sin A + sin B = 1 and cos A + cos B = (3)1/2
A and B < 90o
Find a value for (A+B) ?

2. ## Re: Find the value

Hey Dilan.

Do you know how to relate sin and cos (A+B) to sin(A),sin(B),cos(A),cos(B)?

[Hint - look up a couple of trig identities for more information].

3. ## Re: Find the value

Originally Posted by Dilan
If sin A + sin B = 1 and cos A + cos B = (3)1/2
A and B < 90o
Find a value for (A+B) ?
Try using a couple of the sum to product identities below ...

4. ## Re: Find the value

Let's make a silly assumption and assume $a=b$ (this would be a special case, but who knows, it might pan out).

Then we have:

$2\sin A = 1$ and $2\cos A = \sqrt{3}$

So, $\sin A = \dfrac{1}{2}$ and $\cos A = \dfrac{\sqrt{3}}{2}$

This is a well known angle. Plug it in for $A$, and since we set $B$ equal to the same, it is trivial to find $A+B$.

5. ## Re: Find the value

$\dfrac{\sin{A}+\sin{B}}{\cos{A}+\cos{B}} = \dfrac{2\sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2} \right)}{2 \cos\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right)} = \tan\left(\dfrac{A+B}{2}\right) = \dfrac{1}{\sqrt{3}}$

note that $\tan(30^\circ) = \dfrac{1}{\sqrt{3}}$