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if tan(πcosθ)=cot(πsinθ),the cos,sin are roots of the equation a.4x 2 -4x-1=0 b.4x 2 -2x-1=0 c.8x 2 -4x-3=0 d.none of these

if tan(πcosθ)=cot(πsinθ),the cos,sin are roots of the equation


a.4x2-4x-1=0


b.4x2-2x-1=0


c.8x2-4x-3=0


d.none of these

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Menka,

 

tan(Πcosx) = cot(Πsinx) = tan(Π/2 - Πsinx)

So Πcosx = Π/2-Πsinx

Or cosx = 1/2-sinx.

Squaring, cos2x = 1/4 + sinx2x - sinx

or 2sin2x-sinx-3/4=0

or 8sin2x-4sinx-3 = 0

 

Next also sinx = 1/2-cosx.... similarly squaring you will get 8cos2x-4cosx-3=0.

 

And hence Option (C).

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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