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

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. `sin^(2) theta`B. `cos^(2) theta`C. `tan^(2) theta `D. `tan^(2) 2theta`
Answer» We have `u = cot^(-1) sqrt(cos2 theta)-tan^(-1) sqrt(cos2 theta)` `rarr u = (pi)/(2) - tan^(-1)sqrt(cos 2 theta)-tan^(-1)sqrt(cos 2 theta)` `rarr u = (pi)/(2) -tan^(-1)sqrt(cos 2 theta)/(sin^(2)theta)` ltrbgt `rarr tan(pi)/(2)-u=sqrt(cos 2 theta)/(sin^(2)theta)` `rarr cot u =sqrt(cos^(2) theta)/(sin^(2)theta)` `rarr sin u = (sin^(2) theta)/sqrt(sin^(4)theta + 1 -2 sin^(2) theta)` `rarr sin u =(sin^(2)theta)/(\|1-sin^(2)theta\|)=tan^(2)theta`

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