Assertion (A) : Multiplicative inverse of (sec θ - tan θ) is (sec θ + tan θ). Reason (R) : sec 2 θ - tan 2 θ = 1. 1. A is true, R is false. 2. A is false, R is true. 3. Both A and R are true. 4. Both A and R are false.

Mathematics

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⇒ (sec θ - tan θ)(sec θ + tan θ)

⇒ sec² θ + sec θ. tan θ - tan θ. sec θ - tan² θ

⇒ sec² θ - tan² θ

⇒ 1.

Thus, we can say that :

Multiplicative inverse of (sec θ - tan θ) is (sec θ + tan θ).

∴ Assertion (A) is true.

Solving,

⇒ sec² θ - tan² θ

$\Rightarrow \dfrac{1}{\text{cos}^2 θ} - \dfrac{\text{sin}^2 θ}{\text{cos}^2 θ}$

$\Rightarrow \dfrac{1 - \text{sin}^2 θ}{\text{cos}^2 θ}$

$\Rightarrow \dfrac{\text{cos}^2 θ}{\text{cos}^2 θ}$

⇒ 1.

∴ Reason (R) is true.

Hence, Option 3 is the correct option.

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