Assertion (A): sec² 23° - tan² 23° = 1.

Reason (R): cos 60° = $\dfrac{1}{\sqrt{2}}$

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

According to assertion, sec² 23° - tan² 23° = 1

Solving L.H.S of above equation,

$\Rightarrow \text{sec}^2 23° - \text{tan}^2 23° \\[1em] \Rightarrow \dfrac{1}{\text{cos}^2 23°} - \dfrac{\text{sin}^2 23°}{\text{cos}^2 23°} \\[1em] \Rightarrow \dfrac{1 - \text{sin}^2 23°}{\text{cos}^2 23°} \\[1em] \Rightarrow \dfrac{\text{cos}^2 23°}{\text{cos}^2 23°} \\[1em] \Rightarrow 1.$

Since, L.H.S. = R.H.S.

∴ Assertion (A) is true.

According to standard trigonometric values, the correct evaluation is:

cos 60° = $\dfrac{1}{2}$
​ ∴ Reason (R) is false.

∴ Assertion (A) is true, Reason (R) is false.

Hence, option 1 is the correct option.