If a,{cos ^3}alpha + 3a,cos alpha ,{sin ^2}al | vedclass

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Question

(c) Adding and subtracting the given relation, we get 

$(m + n) = a{\cos ^3}\alpha + 3a\cos \alpha \,{\sin ^2}\alpha $ $ + 3a{\cos ^2}\al

Vedclass · Accepted Answer

$2{a^{2/3}}$

Vedclass · Answer

(c) 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}}$.

If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to

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