If 2y,cos theta = xsin ,theta {rm{ and }}2xse | vedclass

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Question

(a) Given that $2y\,\,\cos 	heta = x\,\sin 	heta $&hellip;..$(i)$

and $2x\,\sec 	heta - y\,\,{m{cosec}}\,	heta = 3$&hellip;..$(ii)$

$ \Rig

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(a) Given that $2y\,\,\cos 	heta = x\,\sin 	heta $&hellip;..$(i)$

and $2x\,\sec 	heta - y\,\,{m{cosec}}\,	heta = 3$&hellip;..$(ii)$

$ \Rightarrow \,\,\frac{{2x}}{{\cos 	heta }} - \frac{y}{{\sin 	heta }} = 3$

$ \Rightarrow \,\,2x\,\sin 	heta - y\,\cos 	heta - 3\,\sin 	heta \cos 	heta = 0$&hellip;..$(iii)$

Solving $(i)$ and $(iii)$, 

we get $y = \sin 	heta $ and $x = 2\,\,\cos 	heta $

Now, ${x^2} + 4{y^2} = 4\,\,{\cos ^2}	heta + 4\,\,{\sin ^2}	heta $ 

$ = 4\,({\cos ^2}	heta + {\sin ^2}	heta ) = 4$.

If $2y\,\cos \theta = x\sin \,\theta {\rm{ and }}2x\sec \theta - y\,{\rm{cosec}}\,\theta = 3,$ then ${x^2} + 4{y^2} = $

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