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Eavaluate lim(x to 0) (sin^(2)2x)/(sin^(...

Eavaluate `lim_(x to 0) (sin^(2)2x)/(sin^(2)4x)`

Text Solution

Verified by Experts

Given, `underset(xto0)"lim"(sin^(2)2x)/(sin^(2)4x) = underset(xto0)"lim"(sin^(2)2x)/(sin2(2x))^(2)`
`=underset(xto0)"lim"(sin^(2)2x)/(2sin2xcos2x)^(2)`
`=underset(xto0)"lim"(1/(4cos^(2)2x))=1/4` `[therefore cos0=1]`
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