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Question

If cos−1(x2−y2x2+y2)=a then dydx=

A
xy
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B
yx
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C
yx
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D
xy
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Solution

The correct option is C yx

Consider the given equation,

cos1(x2y2x2y2)=a

x2y2x2y2=cosa

Differentiate with respect to x

ddx(x2y2x2+y2)=ddxcosa=0

(x2+y2)ddx(x2y2)(x2y2)ddx(x2+y2)(x2+y2)2=0

(x2+y2)(2x2ydydx)(x2y2)(2x+2ydydx)=0

(x2+y2)(2x2ydydx)=(x2y2)(2x+2ydydx)

2x32x2ydydx+2xy22y3dydx=2x3+2x2ydydx2xy22y3dydx

2x2ydydx+2xy2=2x2ydydx2xy2

4x2ydydx=4xy2

dydx=yx

Hence, this is the answer.


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