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Question

If xsin3θ+ycos3θ=sinθcosθ and xsinθ=ycosθ,then (x2+y2) is equal to

A
2
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B
0
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C
3
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D
1
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Solution

The correct option is D 1
Given,

xsinθ=ycosθ

y=xsinθcosθ

xsin3θ+ycos3θ=sinθcosθ

xsin3θ+xsinθcosθ×cos3θ=sinθcosθ

xsin3θ+xsinθcos2θ=sinθcosθ

xsinθ(sin2θ+cos2θ)=sinθcosθ

xsinθ=sinθcosθ

x=cosθ

y=xsinθcosθ=cosθ×sinθcosθ

y=sinθ

x2+y2=cos2θ+sin2θ=1


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