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

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

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Application +4 | -1

a{\cos ^3}\alpha + 3a\,\,\cos \alpha \,\,{\sin ^2} = m\;

and

a\,\,{\sin ^3}\alpha + 3a\,\,{\cos ^2}\alpha \,\,\sin \alpha = n,\;\,\mathrm{then}\;{\left( {m + n} \right)^{2/3}} + \;{\left( {m - n} \right)^{2/3}}\;

is equal to

View answer and explanation

Correct option: C

2{a^{2/3}}

Option C (

2{a^{2/3}}

) is correct because simplifying the given expressions and using the binomial theorem leads to

2{a^{2/3}}