If co s^4 - ^4 = 2/3 , then the value of 2co s^2 - 1 is?

Answer: Option C

$$\begin{array}{rl}& \text{co}{\text{s}}^4\theta -{\sin }^4\theta =\frac{2}{3}\\ & \left[a^4-b^4=\left(a^2-b^2\right)\left(a^2+b^2\right)\right]\\ & \Rightarrow \left(\text{co}{\text{s}}^2\theta +{\sin }^2\theta \right)\left(\text{co}{\text{s}}^2\theta -{\sin }^2\theta \right)=\frac{2}{3}\\ & \left[a^2-b^2=\left(a-b\right)\left(a+b\right)\right]\\ & \Rightarrow 1\times \left(\text{co}{\text{s}}^2\theta -{\sin }^2\theta \right)=\frac{2}{3}\\ & \Rightarrow \text{co}{\text{s}}^2\theta -\left(1-\text{co}{\text{s}}^2\theta \right)=\frac{2}{3}\\ & \left[{\sin }^2\theta =1-\text{co}{\text{s}}^2\theta \right]\\ & \Rightarrow 2\text{co}{\text{s}}^2\theta -1=\frac{2}{3}\end{array}$$