Question

Solve for x:

`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`

Answer 1

`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`

`=>tan^(-1)((2cosx)/(1-cos^2x))=tan^(-1)(2"cosec" x) ""[because 2tan^(-1)x=tan^(-1)(2x/(1-x^2))]`

`=>(2cosx)/(sin^2x) = 2"cosec" x`

`=>(cosx)/(sin^2x) = 1/sinx`

`=>(sinx)/(cosx) = 1`

`=>tanx = 1`

`=> x=pi/4`