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If $x = a \cos^{3} θ \sin^{2} θ, y = a \sin^{3} θ \cos^{2} θ$ and $\frac{{(x^{2} + y^{2})}^{p}}{(x y)^{q}} (p, q, \in N)$ is independent of $θ$ , then

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4p = 5q

4q = 5p

p + q = 9

pq = 20

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detailed solution

Correct option is A

x2+y2p(xy)q=asin2⁡θcos2⁡θ2pa2sin5⁡θcos5⁡θq=a2p(sin⁡θcos⁡θ)4pa2q(sin⁡θcos⁡θ)5qwhich is independent of θ if 4p=5q.

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If x=acos3θsin2θ,y=asin3θcos2θ and x2+y2p(xy)q(p,q,∈N) is independent of θ, then

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If $x = a \cos^{3} θ \sin^{2} θ, y = a \sin^{3} θ \cos^{2} θ$ and $\frac{{(x^{2} + y^{2})}^{p}}{(x y)^{q}} (p, q, \in N)$ is independent of $θ$ , then