Tangents are drawn from the origin to the curve y = sin x. Their points of contact lie on the curve

x²y²=x²+y²

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x²y²=x²-y²

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x²y²=y+x

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None of these

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Solution

The correct option is B
x²y²=x²-y²

The given curve is y =sin x ....(1)
$\Rightarrow \frac{d y}{d x} = c o s x$ .
So,the equation of tangents through the origin (0,0) is
$y - 0 = \frac{d y}{d x} (x - 0) = x c o s x, ∴ \frac{y}{x} = c o s x . . . . (2)$
Squaring and adding equation (1) and (b), we get
$y^{2} + \frac{y^{2}}{x^{2}} = 1. ∴ x^{2} y^{2} = x^{2} - y^{2}$
Hence (b) is the correct answer.

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Tangents are drawn from the origin to the curve y = sin x. Their points of contact lie on the curve

The correct option is B x2y2=x2-y2The given curve is y =sin x ....(1) ⇒dydx=cosx. So,the equation of tangents through the origin (0,0) is y−0=dydx(x−0)=xcosx,∴yx=cosx....(2) Squaring and adding equation (1) and (b), we get y2+y2x2=1.∴x2y2=x2−y2 Hence (b) is the correct answer.