Question

Find the value of tan^–1x – cot^–1x, if `(tan^-1x)^2 - (cot^-1x)^2 = (5π)/8`.

Answer 1

Given, `(tan^-1x)^2 - (cot^-1x)^2 = (5π)/8`

⇒ `[tan^-1x - cot^-1x] [tan^-1x + cot^-1x] = (5π)/8`

⇒ `(tan^-1x - cot^-1x) π/2 = (5π)/8`   ...`[∵ tan^-1x + cot^-1x = π/2]`

⇒ `tan^-1x - cot^-1x = (5π)/8 xx 2/π`

⇒ `tan^-1x - cot^-1x = 5/4`