If sin thita + cos thita=m and sin^3 thita + cos^3 thita=n, then which of the following is correct?

a) m^3 -3m+2n=0.

b) m^3 +3m+2n=0.

c) n^3 -3n+2m=0.

d) m^3 -3m+n=0.

Hi Arnab,

sinx+cosx = m

Squaring we get, 1+2sinxcosx = m^2

or sinxcosx = (m^2 - 1)/2

Now sin^3 x + cos^3 x = (sinx+cosx)(sin^2 x + cos^2 x - sinxcosx)

So n = m(1-[m^2-1]/2)

or m^3 - 3m + 2n = 0

Option (A).

Hope that helps.

Best Regards,

Ashwin (IIT Madras).