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Question
`int 1/(sin^2x cos^2x)dx` = ______.
Options
tan x + cot x + c
– tan x – cot x + c
– tan x + cot x + c
tan x – cot x + c
MCQ
Fill in the Blanks
Solution
`int 1/(sin^2x cos^2x)dx` = tan x – cot x + c.
Explanation:
`int 1/(sin^2x cos^2x)dx`
= `int (sin^2x + cos^2x)/(sin^2x cos^2x)dx`
= `int (sin^2x/(sin^2x cos^2x) + cos^2x/(sin^2x cos^2x))dx`
= `int (sec^2x + "cosec"^2x)dx`
= tan x – cot x + c
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