# Math Help - sum/difference identities

1. ## sum/difference identities

Hi guys, I thought I knew how to do these but I've done this question over and over on an online test that you can self check answers and I can't get the right answer.

Here's the situation:

As, cos(x)=sqrt(1-sin^2(x))

cos(x) =sqrt(7)/(4)
cos(y)=sqrt(-3)/(2)

cos(x+y)=cos(x)cos(y)+sin(x)sin(y)

and I get OVER AND OVER this answer: 3/8-sqrt(21)/8

I spent about half an hour trying to use LaTex to no avail. Sorry.
If someone can grind out something different and post that'd be wonderful.

2. ## Re: sum/difference identities

Hey guys, I just got it.
My formula is cos(x+or-y)=cos(x)cos(y)+or-sin(x)sin(y)
So I assumed that if you were adding angles you'd use addition on the left hand side also, I tried using minus and it worked.. Is that right or is the test wrong?

3. ## Re: sum/difference identities

Originally Posted by camjerlams
left hand side also
*right hand side also

4. ## Re: sum/difference identities

The formula is not correct: cos(A+B) = cosAcosB-sinAsinB
Sin x = 3/4 in first quadrant so cos x will also be positive
sin y = 1/2 in second quadrant hence cos y will be negative.
Just plug in the values to get the result.

5. ## Re: sum/difference identities

Note $\displaystyle \cos{(y)} = -\frac{\sqrt{3}}{2}$, NOT $\displaystyle \frac{\sqrt{-3}}{2}$ as the OP wrote.