The value of `tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))}` is `(sqrt(29))/3` (b) `(29)/3` (c) `(sqrt(3))/(29)` (d) `3/(29)`

Explanation

let `tan a=frac{sin a}{cos a}=frac{frac{7}{2 sqrt5}}{frac{1}{2 sqrt5}}=7`

`b=tan^(-1)7`

`tan b=frac{sin b}{cos b}=frac{frac{4}{sqrt17}}{frac{1}{ sqrt17}}=4`

`tan(tan^(-1)7-tan^(-1)4)`

`=3/29`