A) \[\frac{1}{8}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\]
B) \[\frac{3}{2}\left( a+\frac{1}{a} \right)\]
C) \[\frac{1}{2}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\]
D) \[\frac{1}{3}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\]
Correct Answer: C
Solution :
\[\because \ \cos 3\theta =4{{\cos }^{3}}\theta -3\cos \theta \] \[\therefore \cos 3\theta =4\frac{1}{{{2}^{3}}}{{\left( a+\frac{1}{a} \right)}^{3}}-3\frac{1}{2}\left( a+\frac{1}{a} \right)\] \[\Rightarrow \cos 3\,\theta =\frac{1}{2}\left( a+\frac{1}{a} \right)\,\left[ {{\left( a+\frac{1}{a} \right)}^{2}}-3 \right]\] Þ \[\cos 3\theta =\frac{1}{2}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
