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lim(x->pi/2)(sin(cosx)cosx)/(sinx-cosecx...

`lim_(x->pi/2)(sin(cosx)cosx)/(sinx-cosecx)`

A

0

B

1

C

`-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to (pi)/(2)) (sin (cosx) cos x)/( sin x - "cosec"x) `
`=lim_( x to (pi)/(2)) (sin(cosx))/(cosx) xx lim_(x to (pi)/(2)) (cos^(2)x)/( sin x -(1)/(sin x))=1 xx lim_(x to (pi)/(2)) (cos^(2) x sin x)/( sin^(2)x -1) = lim_( x to (pi)/(2)) (sin x)/(-1)=1`
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