Question

`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to

Options

• `tan x + cot x + c`

• `tan x + "cosec" x + c`

• `- tan x + cot x + c`

• `tan x + sec x + c`

Answer 1

`tan x + cot x + c`

Explanation:

I = `int (sin^2x - cos^2x)/(sin^2 x cos^2x) dx`

= `int ((sin^2x)/(sin^2x cos^2x) - (cos^2x)/(sin^2x cos^2x))`

= `int (1/(cos^2x) = 1/(sin^2x)) dx`

= `int (sec^2x - "cosec"^2x) dx`

= `tan x + cot x + c`