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Derivative of log (sec theta + tan thet...

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

A

0

B

1

C

`(1)/(sqrt(2))`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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` .
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