If f(theta) = sin(tan^(-1)(sintheta/sqrt...

If `f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta)))`, where `-pi/4 lt theta lt pi/4,` then the value of `d/(d(tantheta))\ f(theta)` is

Text Solution

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`f(theta)=sin (tan^(-1)((sin theta)/(sqrt(cos 2theta))))," where "theta in (-(pi)/(4),(pi)/(4))`
`=sin (tan^(-1)((sin theta)/(sqrt(2 cos^(2) theta-1))))=sin (sin^(-1)(tan theta))=tan theta`
`therefore" "(d(tan theta))/(d(tan theta))=1`

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