- #1

Helly123

- 581

- 20

## Homework Statement

##\sin a + \cos b## = ##\frac{-1}{2}##

##\cos a + \sin b## = ##\frac{\sqrt 3}{2}##

0 < a < ##\pi/2##

##\pi/2## < b < ##\pi##

a + b = ? By calculating sin (a+b)

## Homework Equations

## The Attempt at a Solution

I tried :

##\sin a + \cos b =

2sin\frac{(a+b)}{2}cos\frac{(a-b)}{2} = -\frac{1}{2}##

##\cos a + \sin b =2sin\frac{(a+b)}{2}cos\frac{(b-a)}{2} = \frac{\sqrt3}{2}##

I tried to multiple it by ##\sqrt2/2##

##\sin a \cos 45 + \sin 45 \cos b = -\frac{1}{2}\frac{\sqrt 2}{2}##

##\sin 45 \cos a + \sin b \cos 45 = \frac{\sqrt3}{2}\frac{\sqrt 2}{2}##

##\sin a + \cos b = -\frac{1}{2} = \sin 210 = \sin 330 ##

None of this steps get me a clue to find a + b. Can i get a clue?