`tan^(-1)(secx+tanx),(-pi)/(2) lt x lt (pi)/(2)`

Answer

N/a

Explanation

Let `y = tan^(-1)(secx+tanx)`
`:. (dy)/(dx) = (d)/(dx)tan^(-1)(secx+tanx)`
` = (1)/(1+(secx+tanx)^(2)).(d)/(dx)(secx+tanx), [:'(d)/(dx)(tan^(-1)x)= (1)/(1+x^(2))]`
`= (1)/(1+sec^(2)+tan^(2)x+2secx.tanx).[secx.tanx+sec^(2)x]`
`=(1)/((sec^(2)x+sec^(2)x+2secx.tanx)).secx.(secx+tanx)`
` = (1)/(2secx(tanx+secx)).secx(secx+tanx) = 1/2`