If sin x = 7/25 and cos y = 3/5, and x and y are positive acute angles, find:
a) sin (x + y)
b) cos (x - y)
c) tan (x + y)

(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.

77

step-by-step explanation: