Trigonometric identities

Question

If a = 2/5 and b = 7/25 find cos (a+b) without using calculator

Answer 1

cos(a+b) = cosacosb - sinasinb

7-24-25 is a right triangle. 25^2 = 24^2 + 7^2

625 = 576+49

2- sqr21 - 5 is a right triangle

5^2 = 21 + 2^2

25 = 21+4

maybe the problem was miscopied

or should have read something like:

cosa = 3/5 and sinb = 7/25

sina= 4/5 and cosb =24/25

then there is a 3-4-5 right triangle, making the calculations easier

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

= (3/5)(24/25) - (4/5)(7/25)

= 72/125 -28/125

= 44/125

in any event, no matter what the problem was or is, that's the general formula and method