Derivative of ` log (sec theta + tan theta )` with respect top ` sec theta ` at
` theta = (pi)/(4) ` is

Options

A. 0
B. 1
C. `(1)/(sqrt2)`
D. `sqrt2`

Answer

B

Explanation

Let u=log `(sec theta+tan theta) and v=sec theta`. On differentiating both sides w.r.t.x. `theta` we get `(du)/(dtheta)=(1)/((sec theta+tan theta))(sec theta tan theta+sec^(2)theta) and (dv)/(d theta)=sec theta tan theta`
`therefore (du)/(dv)=((du)/(d theta))/((dv)/(d theta))`
`=((sec theta (tan theta+sec theta))/((sec theta+ tan theta)xx sec theta tan theta))=cot theta`
`Rightarrow (du)/(dv)_((theta=(pi)/(4)))=cot""(pi)/(4)=1`