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Mathematics

Choose the correct option. Justify your choice.

1 + tan2A1 + cot2A=\dfrac{\text{1 + tan}^2 A}{\text{1 + cot}^2 A} =

  1. sec2 A

  2. -1

  3. cot2 A

  4. tan2 A

Trigonometric Identities

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Answer

Solving,

⇒1 + tan2A1 + cot2A⇒sec2Acosec2A⇒1cos2A1sin2A⇒sin2Acos2A⇒tan2A.\Rightarrow \dfrac{\text{1 + tan}^2 A}{\text{1 + cot}^2 A} \\[1em] \Rightarrow \dfrac{\text{sec}^2 A}{\text{cosec}^2 A} \\[1em] \Rightarrow \dfrac{\dfrac{1}{\text{cos}^2 A}}{\dfrac{1}{\text{sin}^2 A}} \\[1em] \Rightarrow \dfrac{\text{sin}^2 A}{\text{cos}^2 A} \\[1em] \Rightarrow \text{tan}^2 A.

Hence, Option 4 is the correct option.

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