2 tan -1 (1/3) +cot -1 4 = tan -1 (16/13)

LHS = 2 tan-113 + cot-14=tan-12 × 131 - 19 + tan-114   as, 2 tan-1x = tan-12x1 - x2cot-1x = tan-11x= tan-12/38/9 + tan-114= tan-134 + tan-114= tan-134 + 141 - 34 × 14    as, tan-1x + tan-1y =tan-1x+y1-xy= tan-14/41 - 316= tan-1113/16= tan-11613 = RHS

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2tan inv 1/3 is tan inv 3/4 and cot inv 4 =tan inv 1/4

therefore, tan inv 3/4 +tan inv 1/4=tan inv 16/13.... Proved!

Hope this helps, if there is any doubt feel free to ask!!

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