Question

If xsin^3theta +y cos^3 theta = sin theta . cos thta and x sin thta = y cos theta then prove that x^2+y^2 =1

Answer 1

Hey there !!!!!!!

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xsin³θ+ycos³θ=sinθcosθ

xsinθsin²θ+ycosθcos²θ=sinθcosθ

But according to question xsinθ=ycosθ

So,

ycosθsin²θ+ycosθcos²θ=sinθcosθ

ycosθ(sin²θ+cos²θ)=sinθcosθ

sin²θ+cos²θ=1

ycosθ(sin²θ+cos²θ)=sinθcosθ

ycosθ=sinθcosθ

y=sinθ

xsinθ=ycosθ

But y=sinθ

So,

xsinθ=sinθcosθ

x=cosθ y=sinθ

=x²+y²

=sin²θ+cos²θ

=1

LHS=RHS

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Hope this helped you...............