How do you find the limit of # (1 - cos2Q) / (4Q^2)# as Q approaches 0?

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Answer 1 · 2016-07-03T11:42:01

#1/2#

#lim_{Q to 0} (1 - cos2Q) / (4Q^2)#

using the double angle identity

#= lim_{Q to 0} (1 - (color{red}{1 - 2 sin^2 Q})) / (4Q^2)#

#= lim_{Q to 0} (2 sin^2 Q) / (4Q^2)#

#= lim_{Q to 0} 1/2 ( sin Q) / (Q) (sin Q) / (Q)#

#= 1/2 * 1 * 1#

because #= lim_{z to 0} ( sin z) / (z) = 1# is a well known limit