Q. 45.0( 1 Vote )

Find , when

𝒳 = a cos3θ, 𝒴 = a sin3θ

Answer :

Theorem: y and x are given in a different variable that is θ . We can find by finding and and then dividing them to get the required thing.


=


= a× 3 sin2θ × cosθ (using the chain rule = 3sin2θ× = 2sin2θ × cosθ )


= 3asin2θcosθ . ………..(1)



= a × (3cos2θ)× (-sinθ ) (using chain rule = 2cosθ× = 2 cosθ × (-sinθ ) )


= -3asinθcos2θ.


Dividing (1) and (2), we get


=


= .


= -tanθ


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