A) \[2{{a}^{2}}\]
B) \[2{{a}^{1/3}}\]
C) \[2{{a}^{2/3}}\]
D) \[2{{a}^{3}}\]
Correct Answer: C
Solution :
Adding and subtracting the given relation, we get \[(m+n)=a{{\cos }^{3}}\alpha +3a\cos \alpha \,{{\sin }^{2}}\alpha \]\[+3a{{\cos }^{2}}\alpha .\sin \alpha +a{{\sin }^{3}}\alpha \] \[=a{{(\cos \alpha +\sin \alpha )}^{3}}\] and similarly \[(m-n)=a\,\,{{(\cos \alpha -\sin \alpha )}^{3}}\] Thus, \[{{(m+n)}^{2/3}}+{{(m-n)}^{2/3}}\] \[={{a}^{2/3}}{{\{\cos \alpha +\sin \alpha )}^{2}}+{{(\cos \alpha -\sin \alpha )}^{2}}\}\] \[={{a}^{2/3}}\{2({{\cos }^{2}}\alpha +{{\sin }^{2}}\alpha )\}=2{{a}^{2/3}}\].
You need to login to perform this action.
You will be redirected in
3 sec
