If P_n=cosⁿθ+sinⁿθ,then P_n-P_n-2 =kP_n-4,where

a.k=-1

b.k=1

c.k=-sin²θcos²θ

d.k=4

Hi Menka,

Firstly cosⁿx+sinⁿx = (cos²x+sin²x)(cos^n-2x+sin^n-2x) - sin²xcos^n-2x - cos²xsin^n-2x.

So cosⁿx+sinⁿx = (1)((cos^n-2x+sin^n-2x) - sin²xcos²xcos^n-4x - cos²xsin²xsin^n-4x.

So Pn = Pn-2 - sin²xcos²x(Pn-4).

Hence Pn - Pn-2 = -sin²xcos²x(Pn-4)

Hence Option (C).

Best Regards,

Ashwin (IIT Madras).