Explanation
Differentiate x=acos3θ with respect to θ,
dxdθ=−3acos2θsinθ
Differentiate y=asin3θ with respect to θ,
dydθ=3asin2θcosθ
Now,
dydx=dydθdxdθ
=−3asin2θcosθ3acos2θsinθ
=−tanθ
Then,
1+(dydx)2=1+(−tanθ)2
=1+tan2θ
=sec2θ
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