Formula: 2 Marks
Proof: 2 Marks
Using a3+b3(a+b)(a2−ab+b2) and a3−b3=(a−b)(a2+ab+b2), we have
LHS=Sin3 A+cos3 Asin A+cos A+Sin3 A−cos3 Asin A−cos A=(sin A+cos A)(sin2−sin A cos A+cos2A)(sin A+cos A)+(sin A−cos A)(sin2 A+sin A cos a+cos2A)(sin A−cos A)=1−sin A cos A+1+sin A cos A=2=RHS