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).