If $x\sin^{3}{ heta + y\cos^{3}{ heta = \sin{ heta\cos heta}}}$ and $x\sin{ heta = y\cos heta}$, then $x^{2} + y^{2}$ is

Question

If $x\sin^{3}{	heta + y\cos^{3}{	heta = \sin{	heta\cos	heta}}}$ and $x\sin{	heta = y\cos	heta}$, then $x^{2} + y^{2}$ is

Dr. Abubacker · Accepted Answer

(d)
Given, $x\sin^{3}{	heta + ycos^{3}	heta = \sin{	heta\cos	heta}}$
$\Rightarrow \ \ \ y\cos{	heta\sin^{2}{	heta + y\ cos^{3}	heta}} = \sin{	heta\cos	heta}$
$\lbrack\because\ \ x\sin{	heta = y\cos	heta}brack$
$\Rightarrow \ \ y\cos{	heta\ \left( \sin^{2}{	heta + \cos^{2}	heta} ight) = \sin{	heta\cos	heta}}$
$\Rightarrow \ \ y = \sin	heta$
Now, $x\sin{	heta = \sin{	heta\cos{	heta\ \  \Rightarrow \ \ x = \cos	heta}}}$
$	herefore\ \ \ x^{2} + y^{2} = \cos^{2}{	heta + \sin^{2}{	heta = 1}}$

Q. If $x\sin^{3}{\theta + y\cos^{3}{\theta = \sin{\theta\cos\theta}}}$ and $x\sin{\theta = y\cos\theta}$, then $x^{2} + y^{2}$ is

Explanation

Reviewed by Dr. Abubacker

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