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Q.

If x=a(cos⁡θ+θsin⁡θ),y=a(sin⁡θ−θcos⁡θ) then aθ=

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a

x+y−a

b

x2+y2−a2

c

x2−y2+a2

d

x−y+a

answer is B.

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Detailed Solution

x2+y2=a2cos2⁡θ+sin2⁡θ+θ2sin2⁡θ+θ2cos2⁡θ=a21+θ2⇒aθ=x2+y2−a2
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If x=a(cos⁡θ+θsin⁡θ),y=a(sin⁡θ−θcos⁡θ) then aθ=