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Question
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Options
`log(tanx - sqrt(tan^2x - 1)) + c`
sin–1 (tan x) + c
1 + sin–1 (cot x) + c
`log(tanx + sqrt(tan^2x - 1)) + c`
Solution
`log(tanx + sqrt(tan^2x - 1)) + c`
[ Hint : `int dx/(cosxsqrt(sin^2x - cos^2x)`
= `int (sec2x*dx)/sqrt(tan2x - 1)` ...[Dividing by cos2x]
Put tan x = t].
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