KnowledgeBoat Logo
|

Mathematics

(1 + tan2 A) × cos2 A - 1 is :

  1. 1

  2. -2

  3. 0

  4. 2

Trigonometric Identities

3 Likes

Answer

Solving,

(1+tan2A)×cos2A1(1+sin2Acos2A)×cos2A1(cos2A+sin2Acos2A)×cos2A11cos2A×cos2A1110.\Rightarrow (1 + \text{tan}^2 A) \times \text{cos}^2 A - 1 \\[1em] \Rightarrow \Big(1 + \dfrac{\text{sin}^2 A}{\text{cos}^2 A}\Big) \times \text{cos}^2 A - 1 \\[1em] \Rightarrow \Big(\dfrac{\text{cos}^2 A + \text{sin}^2 A}{\text{cos}^2 A}\Big) \times \text{cos}^2 A - 1 \\[1em] \Rightarrow \dfrac{1}{\text{cos}^2 A} \times \text{cos}^2 A - 1 \\[1em] \Rightarrow 1 - 1 \\[1em] \Rightarrow 0.

Hence, Option 3 is the correct option.

Answered By

2 Likes


Related Questions