Find the value of the following 3(sin⁴θ + cos⁴θ) + 2(sin⁶θ + cos⁶θ) + 12sin²θ.cos²θ = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{The value of }} \cr & {\text{3}}\left( {{{\sin }^4}\theta + {\text{co}}{{\text{s}}^4}\theta } \right) + 2\left( {{{\sin }^6}\theta + {\text{co}}{{\text{s}}^6}\theta } \right) + 12{\sin ^2}\theta .{\text{co}}{{\text{s}}^2}\theta \cr & {\text{Using }}\theta = {0^ \circ } \cr & \because \sin {0^ \circ } = {0^ \circ } \cr & \cos {0^ \circ } = 1 \cr & \Rightarrow 3\left( {0 + {1^4}} \right) + 2\left( {0 + {1^6}} \right) + 12 \times 0 \times 1 \cr & \Rightarrow 3 + 2 \cr & \Rightarrow 5 \cr} $$