`tan(pi/4+1/2cos^-1x)+tan(pi/4-1/2cos^-1x)`, `x!=0` is equal to

Explanation

Let `1/2 cos^-1x = theta=> cos2theta = x`

Then, our expression becomes,

`tan(pi/4+theta)+tan(pi/4-theta)`

`=(1+tantheta)/(1-tantheta) + (1-tantheta)/(1+tantheta)`

`(1+tan^2theta+2tantheta+1+tan^2theta-2tantheta)/(1-tan^2theta)`

`=2((1+tan^2theta)/(1-tan^2theta))`

As `cos2theta = (1-tan^2theta)/(1+tan^2theta)`

So, our expression becomes,

...