You want the limit of y=(1-cos 2x)/x^2 while x approaches 0.
y = (1-cos 2x)/x^2
=> [1 - (1 - 2*(sin x)^2)]/x^2
=> 2*(sin x)^2/x^2
=> 2*(sin x / x)^2
lim x--> 0 (sin x / x) = 1
Using this identity.
lim x--> 0 [ (1-cos 2x)/x^2]
=> lim x--> 0 (2*(sin x/x)]
=> (2)* lim x--> 0 [(sin x/x)]
=> 2*1
=> 2
The required limit is 2.
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