`y=tan^(-1)(x/(1+sqrt(1-x^2)))`

1.	`y=tan^(-1)(x/(1+sqrt(1-x^2)))`
Answer» Correct Answer - `(1)/(2sqrt(1-x^(2)))` `y=tan^(-1)""((x)/(1+sqrt(1-x^(2))))` Put `x= sin theta.` Then, `y=tan^(-1)((sintheta)/(1+sqrt(1-sin^(2)theta)))=tan^(-1)((sintheta)/(1+cos theta))` `=tan^(-1)""(2sin""(theta)/(2)cos""(theta)/(2))/(2cos^(2)""(theta)/(2))=tan^(-1)tan""(theta)/(2)=(theta)/(2)` `"So, "y=(sin^(-1)x)/(2)or(dy)/(dx)=(1)/(2sqrt(1-x^(2)))`

Discussion

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