Find the value of `2cos^(-1)(3/(sqrt(13)))+cot^(-1)(16/63)+1/2cos^(-1)(7/25)`

Explanation

`2cos^-1 (3/sqrt13) + cot^-1 (16/63) +1/2cos^-1 (7/25)`

Now, `cos^-1(3/sqrt13) = tan^-1(2/3)`

`:. 2cos^-1(3/sqrt13) = 2 tan^-1(2/3) = tan^-1((2*(2/3))/(1-(2/3)^2)) = tan^-1((4/3)/(5/9)) = tan^-1(12/5)`

`cot^-1(16/63) = tan^-1(63/16)`

Let `1/2cos^-1(7/25) = tan^-1x`

`=> cos^-1(7/25) = 2tan^-1x`

`=> tan^-1(24/7) = tan^-1((2x)/(1-x^2))`

`=>(2x)/(1-x^2) = 24/7`

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