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

Explanation

`2 tan ^(-1)(cosx)=tan^(-1)(2cosec x)`
`therefore tan^(-1)[(2cos x)/(1-cos^2x)]=tan^(-1)(2cosec x)" "..........[because 2 tan^(-1)x =tan^(-1)((2x)/(1-x^2))]`
`therefore (2cosx)/(1-cos^2x)=2cosecx`
`therefore (2cosx)/(sin^2x)=(2)/(sinx)`
`therefore cos x =sin x`
`therefore x =(pi)/(4)" "........[because sin.(pi)/(4)=cos.(pi)/(4)]`