Question

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

• A. $x^2+y^2=2$
• B. $x^2+y^2=4$
• C. $x^2+y^2=3$
• D. $x^2+y^2=1$

Answer 1

The correct option is D $x^2+y^2=1$

$x{\sin }^{3}A+y{\cos }^{3}A=\sin A\cos A$

$x\sin A\times {sin}^{2}A+y\cos A\times {cos}^{2}A=\sin A\cos A$

$x\sin A\times {sin}^{2}A+x\sin A\times {\cos }^{2}A=\sin A\cos A$

$x\sin A({\sin }^{2}A+{\cos }^{2}A)=\sin A\cos A$

$x\sin A=\sin A\cos A$

$x=\cos A$

$x\sin A=y\cos A$

$\cos A\sin A=y\cos A$

$y=\sin A$

$x^2+y^2={\cos }^{2}A+{\sin }^{2}A=1$