Question

Knowing that 0 <= x <= pi/2, 0 <= y <= pi/2, that sinx = 1/4 and that cosy = 1/5, find sin(x + y), sin(x - y), cos(x + y), cos(x - y)

Answer 1

x and y in first quadrant

if sin x = 1/4, we will need cos x
sin^2 x + cos^2 x = 1
cos x = sqrt( 1-1/16) = sqrt (15/16) = (1/4) sqrt 15

similarly if cos y = 1/5
sin y = sqrt (1- 1/25) =sqrt (24/25)
= (1/5)sqrt 24

now with
sin x = .25, cos x = .25 sqrt 15
and
sin y = .20 sqrt 24, cos y =1/5
Use your trig identities to get the things you want. Watch what quadrant x+y and x-y are in

Answer 2

actually, given the proper values for sin/cos of x and y, the functions of x+y and x-y will work themselves out correctly.