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Evaluate lim(xto pi) (sin^(-1)(1+cosx).s...

Evaluate `lim_(xto pi) (sin^(-1)(1+cosx).sec((x)/(2)))/((x-pi)).`

Text Solution

Verified by Experts

`underset(xto pi)lim(sin^(-1)(1+cosx).sec((x)/(2)))/((x-pi))" "`(0/0 from)
`=underset(xto pi)lim(sin^(-1)(1+cosx))/((1+cosx)).(1+cosx)/(cos((x)/(2))).(1)/((x-pi))`
`=1xxunderset(xto pi)lim(2cos^(2)((x)/(2)))/(cos((x)/(2))).(1)/((x-pi))`
`=underset(xto pi)lim(2cos((x)/(2)))/((x-pi))`
`=underset(xto pi)lim(sin((pi)/(2)-(x)/(2)))/(x/2-pi/2)=-1`
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