If `cos 2theta=(sqrt(2)+1)(cos theta-(1)/(sqrt(2)))`, then the general value of `theta(n in Z)`

Options

A. `f((pi)/(4))=1`
B. `f((pi)/(4))=sqrt(2)`
C. `(d(f(theta)))/(d(cos theta))" at "theta=(pi)/(4)is -2`
D. `f'((pi)/(4))=sqrt(2)`

Explanation

`f(theta)=tan (sin^(-1)sqrt((2)/(3+cos 2theta)))`
`=tan(tan^(-1)sqrt((2)/(1+cos 2e theta)))`
`=sqrt((2)/(1+cos 2 theta))=sec theta`
`rArr" "f((pi)/(4))=sqrt(2)`
`f'(theta)=sec theta tan theta`
`rArr" "f'((pi)/(4))=sqrt(2)`
`(d(f(theta)))/(d(cos theta)):|_(theta=(pi)/4)=((-1)/(cos^(2)theta))_(theta=(pi)/(4))=-2`