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the least positive value of x satisfying...

the least positive value of x satisfying (sin^2 2x + 4 sin^4 x - 4 sin^2x cos^2x)/(4-sin^2(2x)-4sin^2 x)= 1/9 is

Text Solution

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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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