If $$cos^{2} θ - sin^{2} θ = \frac{1}{3}$$ , where 0 ≤ θ ≤ π/2 then the value of $$cos^{4} θ - sin^{4} θ$$ is

Expression : $$cos^{2} θ - sin^{2} θ = \frac{1}{3}$$

We know that $$cos^2 \theta + sin^2 \theta = 1$$

Adding the above two equations, we get :

=> $$2cos^2 \theta = \frac{4}{3}$$

=> $$cos^2 \theta = \frac{2}{3}$$

Squaring both sides,

=> $$cos^4 \theta = \frac{4}{9}$$

Similarly, subtracting those two equations, we get :

=> $$sin^2 \theta = \frac{1}{3}$$

=> $$sin^4 \theta = \frac{1}{9}$$

Now, to find : $$cos^{4} θ - sin^{4} θ$$

= $$\frac{4}{9} - \frac{1}{9}$$

= $$\frac{3}{9} = \frac{1}{3}$$