If cos2x + cos4x = 1, then tan2x + tan4x = ?

Answer: Option B

$$\begin{array}{rl}& {\cos }^{2}x+{\cos }^{4}x=1\\ & \Rightarrow {\cos }^{4}x=1-{\cos }^{2}x\\ & \Rightarrow {\cos }^{4}x={\sin }^{2}x\\ & \Rightarrow {\cos }^{2}x{\cos }^{2}x={\sin }^{2}x\\ & \Rightarrow \text{co}{\text{s}}^{2}x=\text{ta}{\text{n}}^{2}x....(i)\\ & \Rightarrow {\cos }^{4}x=\text{ta}{\text{n}}^{4}x....(ii)\\ & ta{n}^{2}x+{\tan }^{4}x\\ & \text{co}{\text{s}}^{2}x+\text{co}{\text{s}}^{4}x=1\\ & \text{ta}{\text{n}}^{2}x+\text{ta}{\text{n}}^{4}x=1\\ & \left(\text{From eq}\text{. (i) and (ii)}\right)\end{array}$$