1.

The values of x,`0

Answer» `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`
`t=27,3`
`81^(sin^2x) = 27`
`3^(4sin^2x) = 3^3`
so`4sin^2x = 3`
`sin^2x = 3/4`
`sinx = +- sqrt3/2`
`x= pi/3 or -pi/3 = n pi/3`
when `t=3`
`81^(sin^2x) = 3`
`3^(4sin^2x)= 3`
`4sin^2x = 1`
`sinx = +-1/2`
`x= pi/6 or -pi/6`
option A is correct
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