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Question

limxπ2(1sin x) tan x will be equal to _____


A

1

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B

-1

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C

0

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D

None of the above

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Solution

The correct option is C

0


As xπ2 ,sin x1

i.e.(1sin x)0 and

as xπ2 ,tan x

or 1tan x=cot x0

So using this information we can say that xπ2,(1sin x)tan x or(1sin x)cot x comes to 00 form

So we can apply L-Hospitals rule.

limxπ2 (1sin x)cot x=limxπ2ddx(1sin x)ddx(cot x)=limxπ2(cosx)cosec2x

=limxπ2 sin2 x cos x=0

Which is the correct answer.


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