If `x in (0, (pi)/(2))`, then show that `cos^(-1) ((7)/(2) (1 + cos 2 x) + sqrt((sin^(2) x - 48 cos^(2) x)) sin x) = x - cos^(-1) (7 cos x)`

Explanation

`y = cos^(-1) ((7)/(2) (1 + cos 2x) + sqrt((sin^(2) x - 48 cos^(2) x)) sin x)`
`= cos^(-1) ((7 cos x) (cos x) + sqrt(1 - 49 cos^(2) x) sqrt(1 - cos^(2) x))`
`= cos^(-1) (cos x) - cos^(-1) (7 cos x) [ :' cos x lt 7 cos x " for " x in (0, (pi)/(2))]`
`= x - cos^(-1) (7 cos x)`