Assertion (A): tan 30° + sec 30° = cot 30°.

Reason (R): sec θ = $\dfrac{\text{cosec θ}}{\text{cot θ}}$

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 true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Given, tan 30° + sec 30° = cot 30°.

Solving, L.H.S.

⇒ tan 30° + sec 30°

$\Rightarrow \dfrac{1}{\sqrt{3}} + \dfrac{2}{\sqrt{3}}\\[1em] \Rightarrow \dfrac{1 + 2}{\sqrt{3}}\\[1em] \Rightarrow \dfrac{3}{\sqrt{3}}\\[1em] \Rightarrow \sqrt{3}$

Solving, R.H.S. = cot 30° = $\sqrt{3}$

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

∴ Assertion (A) is true.

According to reason (R) : sec θ = $\dfrac{\text{cosec θ}}{\text{cot θ}}$

Solving R.H.S.,

$\Rightarrow \dfrac{\text{cosec θ}}{\text{cot θ}}\\[1em] \Rightarrow \dfrac{\dfrac{1}{\text{sin θ}}}{\dfrac{\text{cos θ}}{\text{sin θ}}}\\[1em] \Rightarrow \dfrac{\text{sin θ}}{\text{sin θ} \times \text{cos θ}}\\[1em] \Rightarrow \dfrac{1}{\text{cos θ}}\\[1em] \Rightarrow \text{sec θ}.$

∴ Reason (R) is true.

∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Hence, option 4 is the correct option.