Question 1061974
Find each exact value if 0 < x < pi/2 and 0 < y < pi/2
Cos(x-y) if sinx= 7/25 and cosy= 2/3

This is what I have so far:
cosa•cosB+sina•sinB
(7/25)(2/3)+(7/25)(sqrt5/3)
14/75+7sqrt5/75
14+7sqrt5/75

I'm not sure if I'm finished with the problem or if I have more steps or if I have just done the problem completely wrong. The answer doesn't match the key so I'm curious as to what I'm doing wrong. Thank you!
<pre>Find each exact value if {{{matrix(1,3, 0 < x < pi/2, and, 0 < y < pi/2)}}}
{{{matrix(1,5, cos(x - y), if, sin (x) = 7/25, and, cos (y) = 2/3)}}}

cos (A - B) = cos A cos B + sin A sin B ---- Difference of 2 angles' formula
cos (x - y) = cos x cos y + sin x sin y ---- Replacing A with x, and B with y 


It's obvious that we need cos x and sin y
{{{sin (x) = 7/25 = O/H = y/r}}}
We see that a 7-24-25 Pythag triple ensues, and therefore, x = 24
We now have: {{{cos (x) = A/H = x/r = 24/25}}}

{{{cos (y) = 2/3 = A/H = x/r}}}
{{{y^2 = r^2 - x^2}}}
{{{y^2 = 3^2 - 2^2}}}
{{{y^2 = 9 - 4}}}_____{{{y = sqrt(5)}}}
We now have: {{{sin (y) = O/H = y/r = sqrt(5)/3}}}

cos (x - y) = cos x cos y + sin x sin y now becomes: 
cos (x - y) = {{{(24/25) * (2/3) + (7/25) * (sqrt(5)/3)}}} ------- Substituting {{{matrix(4,3, 24/25, for, cos (x), 2/3, for, cos (y), 7/25, for, sin (x), sqrt(5)/3, for, sin (y))}}}
Up to this point, you seem to have gotten {{{matrix(1,5, 7/25, for, cos (a), or, cos (x))}}}, but {{{cos (x) = 24/25}}}.
You should be able to complete it, now that you know where your mistake was.


Note that since it was stated that: {{{matrix(1,3, 0 < x < pi/2, and, 0 < y < pi/2)}}}, the angles are in the 1st quadrant.</pre>