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Let f(theta)=sin(tan^(-1)((sintheta)/(s...

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

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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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