If cos2x + cos4x = 1, then tan2x + tan4x = ?
A. 0
B. 1
C. 2tan2x
D. 2tan4x
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\cos ^2}x + {\cos ^4}x = 1 \cr & \Rightarrow {\cos ^4}x = 1 - {\cos ^2}x \cr & \Rightarrow {\cos ^4}x = {\sin ^2}x \cr & \Rightarrow {\cos ^2}x{\cos ^2}x = {\sin ^2}x \cr & \Rightarrow {\text{co}}{{\text{s}}^2}x = {\text{ta}}{{\text{n}}^2}x\,\,\,....(i) \cr & \Rightarrow {\cos ^4}x = {\text{ta}}{{\text{n}}^4}x\,\,\,....(ii) \cr & ta{n^2}x + {\tan ^4}x \cr & {\text{co}}{{\text{s}}^2}x + {\text{co}}{{\text{s}}^4}x = 1 \cr & {\text{ta}}{{\text{n}}^2}x + {\text{ta}}{{\text{n}}^4}x = 1 \cr & \left( {{\text{From eq}}{\text{. (i) and (ii)}}} \right) \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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