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The values of x,0<=x<=pi/2 which satisfi...

The values of x,`0<=x<=pi/2` which satisfies the equation `81^[sin^2x]+81^[cos^2x]=30` are

Text Solution

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`81^(sin^2x) + 81^(1-sin^2x) = 30`
`81^(sin^2x) + 81 xx 81^(-sin^x)= 30`
`81^(sin^2x) + 81/(81^(sin^2x))= 30`
let `t= 81^(sin^2x)`
now, `t + 81/t = 30`
`t^2 -30t +81 = 0`
`t^2 - 27t - 3t + 81=0`
`(t-27)(t-3)= 0`
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