lim x tends to 0=(4sinx-1)2/sin2x
lim as x tends to zero (4sinx - 1)2/sin2x
Now, as x tends to zero, sinx tends to 0.
Hence above limit can be written as,
lim as sinx tends to 0 (4sinx - 1)2/sin2x
Put sinx = y we get,
lim as y tends to 0 (4y - 1)2/y2
= lim as y tends to 0 [(4y - 1)/y]2
= (log4)2 [Using lim as x tends to 0 (ax - 1)/x = loga]
So the required limit is (log4)2.