Adding two cosine waves with different phases

[rapid atlas]

i have cos(x+a) + cos(x+b) = hcos(x+k)
given a and b, i would like to solve for h and k

[gritty sequoia]

note that cos(y) + cos(z) =2cos((y+z)/2)cos((y-z)/2)

U can do the rest

[rapid atlas]

Thank you

.solved