If a cos^3 alpha + 3a cos alpha sin^2 alpha = | vedclass

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(C) Adding the two given equations:$(m + n) = a \cos^3 \alpha + 3a \cos \alpha \sin^2 \alpha + 3a \cos^2 \alpha \sin \alpha + a \sin^3 \alpha$$(m + n)

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$2a^{2/3}$

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(C) Adding the two given equations:$(m + n) = a \cos^3 \alpha + 3a \cos \alpha \sin^2 \alpha + 3a \cos^2 \alpha \sin \alpha + a \sin^3 \alpha$$(m + n) = a(\cos \alpha + \sin \alpha)^3$Subtracting the two given equations:$(m - n) = a \cos^3 \alpha + 3a \cos \alpha \sin^2 \alpha - 3a \cos^2 \alpha \sin \alpha - a \sin^3 \alpha$$(m - n) = a(\cos \alpha - \sin \alpha)^3$Now,calculating $(m + n)^{2/3} + (m - n)^{2/3}$:$= [a(\cos \alpha + \sin \alpha)^3]^{2/3} + [a(\cos \alpha - \sin \alpha)^3]^{2/3}$$= a^{2/3}(\cos \alpha + \sin \alpha)^2 + a^{2/3}(\cos \alpha - \sin \alpha)^2$$= a^{2/3}[(\cos^2 \alpha + \sin^2 \alpha + 2 \sin \alpha \cos \alpha) + (\cos^2 \alpha + \sin^2 \alpha - 2 \sin \alpha \cos \alpha)]$$= a^{2/3}[1 + 1] = 2a^{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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