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tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x)) wher...

`tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x))` where `x!=0,` is equal to

Text Solution

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Let `ax = tan theta`
`rArr tan^(-1) ((sqrt(1 + a^(2) x^(2)) -1)/(ax)) = tan.^(-1) ((sqrt(1 + tan^(2) theta) - 1)/(tan theta))`
`= tan.^(-1) ((sec theta -1)/(tan theta))`
`= tan.^(-1) ((1- cos theta)/(sin that))`
`= tan^(-1) (tan. (theta)/(2)) = (theta)/(2)`
`= tan^(-1) ax)/(2)`
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