A) \[\frac{{{e}^{2}}+1}{2e}\]
B) \[\frac{{{e}^{4}}+1}{2{{e}^{2}}}\]
C) \[\frac{{{({{e}^{2}}-1)}^{2}}}{2{{e}^{2}}}\]
D) \[\frac{{{({{e}^{2}}+1)}^{2}}}{2{{e}^{2}}}\]
Correct Answer: C
Solution :
[c] We know that \[\frac{{{e}^{x}}+{{e}^{-x}}}{2}=1+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{4}}}{4!}+\frac{{{x}^{6}}}{6!}+....\] keeping \[x=2,\] we get Expression \[=\frac{1}{2}\left[ \frac{{{e}^{2}}+{{e}^{-2}}}{2} \right]-1=\frac{{{({{e}^{2}}-1)}^{2}}}{2{{e}^{2}}}\]
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