If θ be a positive acute angle satisfying cos2θ + cos4θ = 1, then the value of tan2θ + tan4θ is?
A. $$\frac{3}{2}$$
B. 1
C. $$\frac{1}{2}$$
D. 0
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{co}}{{\text{s}}^2}\theta + {\text{co}}{{\text{s}}^4}\theta = 1 \cr & \Rightarrow {\text{co}}{{\text{s}}^4}\theta = 1 - {\cos ^2}\theta \cr & \Rightarrow {\text{co}}{{\text{s}}^4}\theta = {\sin ^2}\theta \cr & \Rightarrow {\cos ^2}\theta .{\cos ^2}\theta = {\sin ^2}\theta \cr & \Rightarrow {\cos ^2}\theta = \frac{{{{\sin }^2}\theta }}{{{{\cos }^2}\theta }} \cr & \Rightarrow {\text{co}}{{\text{s}}^2}\theta = {\text{ta}}{{\text{n}}^2}\theta \cr & \Rightarrow {\text{ta}}{{\text{n}}^2}\theta + {\text{ta}}{{\text{n}}^4}\theta \cr & \Rightarrow {\text{co}}{{\text{s}}^2}\theta + {\text{co}}{{\text{s}}^4}\theta = 1 \cr} $$Join The Discussion
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