Solve the equation `2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)`

Answer

`x = (pi)/(4)`

Explanation

`2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)`
`rArr tan^(-1) ((2 cos x)/(1 -cos^(2) x)) = tan^(-1) (2 cosec x) " " [ :' 2 tan^(-1) x = tan^(-1).(2)/(1- x^(2))`
`rArr (2 cos x)/(1- cos^(2) x) = 2 cosec x`
`rArr (2 cos x)/(sin^(2) x) = (2)/(sin x)`
`rArr cos x = sin x`
`rArr tan x = 1`
`:. x = (pi)/(4)`