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Question
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Options
tan x – x + c
x + tan x + c
x – tan x + c
– x – cot x + c
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Solution
x – tan x + c
[ Hint : `int (cos2x - 1)/(cos2x + 1)*dx`
= `int (-(1 - cos2x))/(1 + cos^2x)*dx`
= `int (-2sin^2x)/(2cos^2x)*dx`
= `int (sec^2x - 1)*dx`
= – tan x + x + c.
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