If `u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta)` then sin u=A. `tan theta //2`B. `tan^(2) theta//2`C. `cot theta//2`D. `cot^(2) theta//2`

If `u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta)` then sin u=A.

1.	If `u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta)` then sin u=A. `tan theta //2`B. `tan^(2) theta//2`C. `cot theta//2`D. `cot^(2) theta//2`
Answer» We have `u= cot^(-1)sqrt(cos theta)-tan^(-1)sqrt(cos theta)` `rarr u = (pi)/(2) -2 alpha where alpha =tan^(-1)(sqrt(cos theta))` `rarr sin u =cos 2 alpha` `rarr sin u =(1-tan^(2)alpha)/(1+tan^(2) alpha)=(1-cos theta)/(1+cos theta)=tan^(2)(theta)/(2)`

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