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underset(xto pi/4)lim(cot^3x-tanx)/(cos(...

`underset(xto pi/4)lim(cot^3x-tanx)/(cos(x+pi/4))` is

A

`4sqrt(2)`

B

8

C

4

D

`8sqrt(2)`.

Text Solution

Verified by Experts

The correct Answer is:
B
`Lt_(x to (pi)/(4))(cot^3 x-tan x)/(cos(x+(pi)/(4)))`
Given limit is in `(0)/(0)` form.
Applying L.H.Rule. `Lt_(x+(pi)/(4))(3cot^2x(cosec^2x)-sec^2x)/(-sin(x+(pi)/(4)))=8`
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