Find the value of A if

If sec 2A = cosec (A - 27°) where 2A is an acute angle, find the measure of ∠A.

Find the value of θ (0° < θ < 90°) if :

cos 63° sec (90° - θ) = 1

If A, B and C are the interior angles of a △ABC, show that :

(i) cos $\dfrac{A + B}{2}$ = sin $\dfrac{C}{2}$

(ii) tan $\dfrac{C + A}{2}$ = cot $\dfrac{B}{2}$

The value of $\dfrac{\text{tan 30°}}{\text{cot 60°}}$ is

1. $\dfrac{1}{\sqrt{2}}$

2. $\dfrac{1}{\sqrt{3}}$

3. $\sqrt{3}$

4. 1