1.

Solev `(sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-sin^(2) 2x-4 sin^(2) x)=1/9`.

Answer» We have
`(sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-4 sin^(2) x- sin^(2) 2x)=1/9`
`rArr (4 sin^(4)x)/(4 cos^(2) x-4 sin^(2) x cos^(@) x)=1/9`
`rArr sin^(4) x/cos^(4) x=1/9`
`rArr tan^(2) x=(1/sqrt(3))^(2)=("tan"pi/6)^(2)`
`rArr x=n pi pm pi/6`


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