lim x tends to 0=(4^{sinx}-1)^{2}/sin^{2}x

lim as x tends to zero (4^{sinx} - 1)^{2}/sin^{2}x

Now, as x tends to zero, sinx tends to 0.

Hence above limit can be written as,

lim as sinx tends to 0 (4^{sinx} - 1)^{2}/sin^{2}x

Put sinx = y we get,

lim as y tends to 0 (4^{y} - 1)^{2}/y^{2}

= lim as y tends to 0 [(4^{y} - 1)/y]^{2}

= (log4)^{2 }[Using lim as x tends to 0 (a^{x} - 1)/x = loga]

So the required limit is (log4)^{2}.

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