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प्रश्न
Find `"dy"/"dx"` of the following function:
x = a cos3θ, y = a sin3θ
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उत्तर
x = a cos3θ, y = a sin3θ
we have x = a cos3θ; y = a sin3θ
Now, ∴ `"dx"/("d"theta) = - 3"a" cos^2theta sin theta and "dy"/("d"theta) = 3"a" sin^2theta cos theta`
Therefore `"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d"theta))`
`= (3"a"sin^2theta cos theta)/(-3"a" cos^2theta sin theta)`
`= - (sin theta)/(cos theta)`
= - tan θ
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