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Evaluate lim(xto(pi)/(4)) (1-sin2x)/(1+c...

Evaluate `lim_(xto(pi)/(4)) (1-sin2x)/(1+cos4x).`

Text Solution

Verified by Experts

The correct Answer is:
`1//4`
`underset(xto(pi)/(4))lim(1-sin2x)/(1+cos4x)" "`(0/0 form)
`=underset(xto(pi)/(4))lim(sinx-cosx)^(2)/(2cos^(2)2x)" "`(0/0 form)
`=underset(xto(pi)/(4))lim(sinx-cosx)^(2)/((cos^(2)x-sin^(2)x)^(2))" "`(0/0 form)
`=underset(xto(pi)/(4))lim(1)/(2(cosx+sinx)^(2))=1/4`
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