Aspire Faculty ID #15186 · Topic: JAMIA MCA 2017 · Just now
JAMIA MCA 2017

If $x=a\cos^{2}\theta\sin\theta$ and $y=a\sin^{2}\theta\cos\theta$, then $(x^{2}+y^{2})^{3}$ is …

Solution

$x^{2}+y^{2}=a^{2}\sin^{2}\theta\cos^{2}\theta$. So $(x^{2}+y^{2})^{3}=a^{6}\sin^{6}\theta\cos^{6}\theta = a^{2}(a^{4}\sin^{6}\theta\cos^{6}\theta)=a^{2}x^{2}y^{2}$.
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