Answer:
(a) 117/125.
(b) 4/5
(c) 117/44.
Step-by-step explanation:
Consider < x , If it's sine is 7/25 then its part of the right triangle where 25^2 = z^2 + 7^2 so z = sqrt (25^2 - 7^2) = 24 ( the other leg = 24 units).
Therefore cos x = 24/25.
Consider < y, cos y = 3/5 , then z^2 = sqrt(5^2 - 3^2) = 4 (other leg = 4).
Therefore sin y = 4/5.
(a) sin (x + y) = sin x cos y + cos x sin y
= 7/25 * 3/5 + 24/25 * 4/5
= 117/125.
(b) cos (x - y) = cos x cos y + sin x sin y
= 24/25 * 3/5 + 7/25 * 4/5
= 4/5.
(c) cos (x + y) = 24/25 * 3/5 - 7/25 * 4/5
= 44/125.
So tan (x + y)
= sin (x + y) / cos (x + y)
= 117/125 / 44/125
= 117/44.
