`"Let "f(theta)=sin (tan^(-1)((sin theta)/(sqrt(cos 2theta))))," where "-(pi)/(4)ltthetalt(pi)/(4)." Then the value of "(d)/(d(tan theta))(f(theta))` is -

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

We have,
`f(theta)=sin{tan^(-1)((sintheta)/(sqrt(1-2sin^(2)theta)))}`
`implies" "f(theta)=sin{sin^(-1)((sintheta)/(sqrt(sin^(2)theta+1-2sin^(2)theta)))}`
`implies" "f(theta)=sin{sin^(-1)(tantheta)}=tantheta`
`:." "(d)/(d(tantheta))(f(theta))=1`