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

Options

A. 0
B. 1
C. `(1)/(sqrt(2))`
D. `sqrt(2)`

Answer

B

Explanation

Let ` u = log ( sec theta + tan theta ) and v = sec theta `
On differentiatng both sides w.r.t.`theta ` , we get
`(du)/(d theta ) = (1) /((sec theta + tan theta) ) (sec theta tan theta + sec^(2) theta )`
and ` (dv)/(d theta ) = sec theta tan theta `
` therefore (du)/(dx) = ((du)/(d theta) )/((dv)/(d theta)) = (sec theta (tan theta + sec theta))/((sec theta + tan theta )xxsec theta tan theta ) = cot theta `
` rArr (du)/(dv)""_((theta = (pi)/(4)))= cot ""(pi)/(4)= 1` .