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If x in (0, 1), then find the value of t...

If `x in (0, 1)`, then find the value of `tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(2)`
`tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`
`= (pi)/(2) - tan^(-1) ((2x)/(1 - x^(2))) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`
`= (pi)/(2) - 2tan^(-1) x + 2tan^(-1) x " " ("as " x in (0, 1))`
`= (pi)/(2)`
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