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?

1 Answer
Jun 7, 2016

Answer:

#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).#