If cos²θ - sin²θ = $$\frac{1}{3}{\text{,}}$$ where 0 ≤ θ ≤ $$\frac{\pi }{2}{\text{,}}$$ then the value of cos⁴θ - sin⁴θ is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{co}}{{\text{s}}^2}\theta - {\sin ^2}\theta = \frac{1}{3}{\text{ }}\left( {{\text{Given}}} \right) \cr & {\text{co}}{{\text{s}}^2}\theta + {\sin ^2}\theta = 1{\text{ }}\left( {{\text{Property}}} \right) \cr & \left( {{\text{co}}{{\text{s}}^2}\theta - {{\sin }^2}\theta } \right)\left( {{\text{co}}{{\text{s}}^2}\theta + {{\sin }^2}\theta } \right) = \frac{1}{3} \times 1 \cr & {\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{1}{3} \cr & \therefore \left( {\left( {{a^2} + {b^2}} \right)\left( {{a^2} - {b^2}} \right) = {a^4} - {b^4}} \right) \cr} $$