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find domain of the definition y=log_{3}(x^{2}+1)/(sin^{2}x - sinx + 0.25)

_{3}(x

^{2}+ 1)/(sin

^{2}x - sinx + 0.25)

Wkt, x

^{2}>= 0 which implies that x

^{2}+1 >= 1.

So, the expression in the numerator of the given function (i.e log

_{3}(x

^{2}+ 1)) is always defined for all real values of x.

Also, the denominator of the function should not be zero.

So, sin

^{2}x - sinx + 0.25 is not equal to zero.

i.e (sinx - 1/2)

^{2}is not equal to zero.

i.e sinx must not be equal to 1/2.

which implies that x is not equal to n(pi) + (-1)

^{n}((pi)/6), where n is an integer.

So the domain of the function is R - {n(pi) + (-1)

^{n}((pi)/6) | n is an integer}.

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