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Prove that: sin^(-1)(12)/(13)+cos^(-1)4/...

Prove that: `sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`

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Let, `sin^-1(12/13) = x and cos^-1(4/5) = y and tan^-1(63/16)=z->(1)`
Then,`sin x = 12/13 and cos y = 4/5`
`tan x = 5/12 and tan y = 3/4`
`x = tan^-1(5/12) and y = tan^-1(3/4)->(2)`
From (1) and (2),
`sin^-1(12/13) + cos^-1(4/5) = tan^-1(12/5)+tan^-1(3/4) `
We know, `tan^-1x+tan-^-1y = tan^-1((x+y)/(1-xy))`
`tan^-1(12/5)+tan^-1(3/4) = tan^-1((12/5+3/4)/(1-12/5**3/4))`
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