Answer:
10 cos x +8sqrt2 = 8cos x +7 sqrt2 collect like times together to have
10cosx-8cosx = 8√2 - 7√2 then solve to have
2cosx = √2 divide by two in both sides
cosx=√2/2 but 2= √2 *√2
so cosx= √2/(√2 * √2) so cos x =1/√2 but we know that cos inverse of 1/√2= 45 thus cos 45 = 1/√2 thus x = 45
