Suppose sin(x) - sin(y) = sqrt{7/3}, cos(x) + cos(y) = 1. Find cos(x + y).

[MethMath11]

isnt cos (a + b) = cos a cos b - sin a sin b? so what's the point on giving sin a - sin b = x?

 

[Deleted member 4993]

isnt cos (a + b) = cos a cos b - sin a sin b? so what's the point on giving sin a - sin b = x?

Did you try to solve it - ignoring the given (sin a - sin b = x)? What did you get?

 

[MethMath11]

Did you try to solve it - ignoring the given (sin a - sin b = x)? What did you get?

tried to solve it, dont know where to begin with. i have tried elaborating cos a + cos b = 2 cos (a + b)/2 cos (a-b)/2 and the sin a + sin b too, end up ruining everything, that's why i post this thread

 

[MarkFL]

We are given:

[MATH]\sin(x)-\sin(y)=\sqrt{\frac{7}{3}}[/MATH]
[MATH]\cos(x)+\cos(y)=1[/MATH]
If we square both equations, we get:

[MATH]\sin^2(x)-2\sin(x)\sin(y)+\sin^2(y)=\frac{7}{3}[/MATH]
[MATH]\cos^2(x)+2\cos(x)\cos(y)+\cos^2(y)=1[/MATH]
Now, add these last two equations and see where that leads...