If tan–1 x + tan–1 y = 4π/5, then cot–1x + cot–1 y equals


We know that,



We have,


tan–1 x + tan–1 y = 4π/5 … (1)


Let, cot–1x + cot–1 y = k … (2)


Adding (1) and (2) –



Now, tan–1 A + cot–1 A = π/2 for all real numbers.


So, (tan–1 x + cot–1 x) + (tan–1y + cot–1 y) = π … (4)


From (3) and (4), we get,




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