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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
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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