Question

Given: cos(x/4)=a and cos(y/3)+b, how do you find cos(x/4+y/3) in terms of a and b?

Answer 1

`ab - (1 - a^2)^(1/2)(1-b^2)^(1/2)`

Explanation:

Use trig identity:
cos (a + b) = cos a.cos b - sin a.sin b.
`cos (x/4 + y/3) = cos (x/4).cos (y/3) - sin (x/4).sin (x/3) =`
Since `cos (x/4) = a` and `cos (y/3) = b`, then -->
cos `(x/4 + y/3) = ab - sin (x/4).sin (y/3)`.
Find `sin (x/4)` and `sin (y/3)`
`sin^2 (x/4) = 1 - a^2 -> sin (x /4) = (1 - a^2)^(1/2)`
`sin^2 (y/3) = 1 - b^2 --> sin (y/2) = (1 - b^2)^(1/2)`
Finally,
`cos (x /4 + y/3) = ab - (1 - a^2)^(1/2)(1- b^2)^(1/2).`