A) \[\frac{1}{1-{{a}^{2}}{{b}^{2}}}\]
B) \[\frac{a}{1-{{a}^{2}}{{b}^{2}}}\]
C) \[a\]
D) \[\frac{a}{\sqrt{1-{{a}^{2}}{{b}^{2}}}}\]
Correct Answer: C
Solution :
Harmonic mean of given numbers \[=\frac{2\left( \frac{a}{1-ab} \right)\left( \frac{a}{1+ab} \right)}{\frac{a}{1-ab}+\frac{a}{1+ab}}\] \[=\frac{2{{a}^{2}}}{a(1+ab)+a(1-ab)}\] \[=\frac{2{{a}^{2}}}{a+{{a}^{2}}b+a-{{a}^{2}}b}=\frac{2{{a}^{2}}}{2a}=a\]
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