Let sinx+cosx=p ...(i) sin3x+cos3x=q ...(ii) On cubing Eq. (i) both sides sin3x+cos3x+3sinxcosx(sinx+cosx)=p3 Put sin3x+cos3x=q from equation (ii) ⇒ q+3sinxcosx(p)=p3 ...(iii) On squaring Eq. (i) both sides, we get sin2x+cos2x+2sinxcosx=p2 ⇒ sinxcosx=