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

Question

Philoid · Accepted Answer

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,

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