InterviewSolution
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InterviewSolution
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`d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))]` isA. -1B. `(1)/(2)`C. `-(1)/(2)`D. 1 |
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Answer» `"Let "y=sin^(2)cot^(-1){sqrt((1-x)/(1+x))}` `"Put "x=cos theta or theta = cos^(-1)x` `therefore" "y=sin^(2)cot^(-1){sqrt((1-cos theta)/(1+cos theta))}= sin ^(2) cot^(-1) (tan""(theta)/(2))` `=sin^(2)((pi)/(2)-(theta)/(2))` `=cos^(2)((theta)/(2))` `=(1+ cos theta)/(2)` `=(1+x)/(2)` `therefore" "(dy)/(dx)=(1)/(2)` |
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