यदि x{sin ^3}alpha + y{cos ^3}alpha = sin alp | vedclass

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Question

यहाँ $x\,{\sin ^3}\alpha  + y\,{\cos ^3}\alpha  = \sin \,\alpha \,\cos \,\alpha $&hellip;..$(i)$

एवं $x\,\sin \,\alpha  - y\,\cos \,

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$1$

Vedclass · Answer

यहाँ $x\,{\sin ^3}\alpha  + y\,{\cos ^3}\alpha  = \sin \,\alpha \,\cos \,\alpha $&hellip;..$(i)$

एवं $x\,\sin \,\alpha  - y\,\cos \,\alpha  = 0$&hellip;..$(ii)$

अब $(ii)$ से, $x\,\sin \,\alpha  = y\,\cos \,\alpha $

यह मान $(i)$ में रखने पर,

$ \Rightarrow \,\,y\,\cos \alpha \,{\sin ^2}\alpha  + y\,{\cos ^3}\alpha  = \sin \,\alpha \,\cos \,\alpha $

$ \Rightarrow \,\,y\,\cos \alpha \,\left\{ {{{\sin }^2}\alpha  + {{\cos }^2}\alpha } \right\} = \sin \,\alpha \,\cos \,\alpha $

$ \Rightarrow \,\,y\,\cos \,\alpha  = \sin \,\alpha \,\cos \,\alpha \,$

$\Rightarrow \,\,y = \sin \,\alpha $ एवं $x = \cos \,\alpha $

अत:, ${x^2} + {y^2} = {\sin ^2}\alpha  + {\cos ^2}\alpha  = 1.$

यदि $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ व $x\sin \alpha - y\cos \alpha = 0,$ तो ${x^2} + {y^2} = $

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