Question

If sin(x) = 1/3 and sec(y) = 29/21, where x and y lie between 0 and 𝜋/2, evaluate the expression.

cos(x + y)

Answer 1

So both angles are in quad I, that makes it quite simple.

sinx = 1/3,
so we have x^2 + y^2 = r^2
1 + x^2 = 9
x = √8 = 2√2 , (the x is not the same x as the angle)
then cosx = 2√2/3

secy = 29/21 or cosy = 21/29
y^2 + 21^2 = 29^2
y = √400 = 20 ---> siny = 20/29

cos(x+y) = cosxcosy - sinxsiny
= (2√2/3)(21/29) - (1/3)(20/29)
= (42√2 - 20)/87