Question

sin⁶ A + cos⁶ A + 3 sin² A cos² A =
(a) 0
(b) 1
(c) 2
(d) 3

Answer 1

(b) 1

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ {\sin }^{6}A+{\cos }^{6}A+3\left({\sin }^{2}A\right)\left({\cos }^{2}A\right) \\ ={\left({\sin }^{2}A\right)}^3+{\left({\cos }^{2}A\right)}^3+3\left({\sin }^{2}A\right)\left({\cos }^{2}A\right)\times 1 \\ ={\left({\sin }^{2}A\right)}^3+{\left({\cos }^{2}A\right)}^3+3\left({\sin }^{2}A\right)\left({\cos }^{2}A\right)\left({\sin }^{2}A+{\cos }^{2}A\right) \\ ={\left({\sin }^{2}A+{\cos }^{2}A\right)}^3 \\ =1^3=1 \end{gathered}$$