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Question
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) 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
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Solution
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to tan x + cot x + C.
Explanation:
Let I = `int (sin^2 x - cos^2 x)/(sin^2 x cos^2 x) dx`
`= int ((sin^2 x)/(sin^2 x cos^2 x) - (cos^2 x)/(sin^2 x cos^2 x))`
`= int (1/(cos^2 x) - 1/(sin^2 x)) dx`
`= int (sec^2 x - cosec^2 x) dx`
`= tan x + cot x + C`
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