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lim(x to 0){(1+tanx)/(1+sinx)}^("cosec x...

`lim_(x to 0){(1+tanx)/(1+sinx)}^("cosec x")` is equal to

A

`1//e`

B

1

C

e

D

`e^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_(x to 0){(1+tan x)/(1+sin x)}`
`=lim_(x to 0)[([(1+(sinx)/(cosx))^((cosx)/(sinx))]^(1//cos x))/((1+sin x)^((1)/(sinx)))]=e^(lim_(x to 0)(1)/(cos x))/(e )=(e )/(e )=1`
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