Question

`int 1/(sin x * cos x)` dx = ?

विकल्प

• log |sin x| + c

• log |cos x| + c

• log |tan x| + c

• log |sec x| + c

Answer 1

log |tan x| + c

Explanation:

`int 1/(sin x * cos x)` dx

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

`= int [(sin^2x)/(sin x cos x) + (cos^2x)/(sin x cos x)]`dx

= ∫(tan x + cot x)dx

= log |sec x| + log |sin x| + c

= log |sec x × sin x| + c

= log |tan x| + c