Cos(x+y)=4/5 sin( x-y) =5/13 find tan2x where x, y lie bet 0,45degr

x+y = cos^-1(4/5)x-y = sin^-1(5/13)Now convert them in term of tan^-1 by making triangle after converting to tan^-1 we get x+y = tan^-1 (3/4).…...........(1) x-y = tan^-1 (5/12)..............(2) Now add both of them2x = tan^-1(3/4) + tan^-1(5/12)taking tan on both sideand also apply (tan^-1a + tan-^1b) formulatan(2x) = tan[tan^-1{(3/4 + 5/12)/(1-3/4×5/12)}]tan(2x) = 56/33