(i) Given as 2tan-1(3/4) – tan-1(17/31) = π/4
Considering L.H.S.
= 2tan-1(3/4) - tan-1(17/31)
As we know that
= tan-1(625/625)
= tan-1 (1)
= π/4 = R.H.S.
Therefore, 2tan-1(3/4) - tan-1(17/31) = π/4
Hence, proved
(ii) Given as 2tan-1(1/2) + tan-1(1/7) = tan-1(31/17)
Considering L.H.S.
= 2tan-1(1/2) + tan-1(1/7)
As we know
= R.H.S.
Therefore, 2tan-1(1/2) + tan-1(1/7) = tan-1(31/17)
Hence, proved