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Evaluate, lim(xto(pi//6)) (cot^(2)x-3)/(...

Evaluate, `lim_(xto(pi//6)) (cot^(2)x-3)/("cosec"x-2)`

A

`2`

B

`3`

C

`4`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `underset(xto(pi//6))"lim"(cot^(2)x-3)/("cosec"x-2) = underset(xto(pi//6))"lim"("cosec"^(2)x-1-3)/("cosec"x-2)` `[therefore"cosec"^(2)x=1+cot^(2)x]`
`=underset(xto(pi//6))"lim"("cosec"^(2)x-4)/("cosec"x-2)=underset(xto(pi//6))"lim"(("cosec"x)^(2)-(2)^(2))/("cosec"x-2)`
`=underset(xto(pi//6))"lim"(("cosec"x+2)("cosec"x-2))/("cosec"x-2)`
`="cosec"pi/6+2=2+2=4`
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