If x = a cos^3 theta and y = b sin^3 theta,th | vedclass

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(C) Given $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$. Dividing by $a$ and $b$ respectively,we get $\frac{x}{a} = \cos^3 	heta$ and $\frac{y}{b}

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$(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$

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(C) Given $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$. Dividing by $a$ and $b$ respectively,we get $\frac{x}{a} = \cos^3 	heta$ and $\frac{y}{b} = \sin^3 	heta$. Taking the power of $1/3$ on both sides,we get $(\frac{x}{a})^{1/3} = \cos 	heta$ and $(\frac{y}{b})^{1/3} = \sin 	heta$. Squaring both sides,we get $(\frac{x}{a})^{2/3} = \cos^2 	heta$ and $(\frac{y}{b})^{2/3} = \sin^2 	heta$. Adding these two equations,we get $(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = \cos^2 	heta + \sin^2 	heta$. Since $\cos^2 	heta + \sin^2 	heta = 1$,we have $(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$.

List-$I$	List-$II$
$(I)$ $\sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} + \dots + \sin^2 90^{\circ}$	$(A)$ $0$
$(II)$ $\tan^2 5^{\circ} \cdot \tan^2 10^{\circ} \cdot \tan^2 15^{\circ} \dots \tan^2 85^{\circ}$	$(B)$ $\frac{19}{2}$
$(III)$ $\cos^2 5^{\circ} + \cos^2 10^{\circ} + \cos^2 15^{\circ} + \dots + \cos^2 180^{\circ}$	$(C)$ $18$
$(IV)$ $\cot 5^{\circ} + \cot 10^{\circ} + \cot 15^{\circ} + \dots + \cot 175^{\circ}$	$(D)$ $1$
	$(E)$ $-1$

If $x = a \cos^3 \theta$ and $y = b \sin^3 \theta$,then:

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