Question

`int(dx)/(a^(2)sin^(2)x+b^(2)cos^(2)x)` is equal to
A. `(1)/(ab)tan^(-1)((a tanx)/(b))+C`
B. `(1)/(b)tan^(-1)((atanx)/(b))+C`
C. `(b)/(a)tan^(-1)((btanx)/(a))+C`
D. None of these

Answer 1

Correct Answer - A
`int(dx)/(a^(2)sin^(2)x+b^(2)cos^(2)x)`
`=int(sec^(2)xdx)/(a^(2)tan^(2)x+b^(2))=(1)/(a^(2))int(dt)/(t^(2)+((b)/(a))^(2))`
where, t = tan x
`=(1)/(a^(2)).(a)/(b)tan^(-1)(t)/(b//a)+C=(1)/(ab).tan^(-1){(a(tanx))/(b)}+C`