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Derivative of ` log (sec theta + tan theta )` with respect top ` sec theta ` at ` theta = (pi)/(4) ` is |
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Answer» Correct Answer - B 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` |
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