Question

Solve for x:

5tan^–1x + 3cot^–1x = 2π

Answer 1

5tan^–1x + 3cot^–1x = 2π

`\implies 5tan^-1x + 3(π/2 - tan^-1x)` = 2π

`\implies` 5tan^–1x – 3tan^–1x = `2π - (3π)/2`

2tan^–1x = `π/2`

tan^–1x = `π/4`

x = `tan  π/4`

= 1