Show that :

$\dfrac{\text{cos}^2 (45° + θ) + \text{cos}^2 (45° - θ)}{\text{tan (60° + θ) \text{tan (30° - θ)}}} = 1$

Find the value of A if

sin 3A = cos (A - 6°), where 3A and A - 6° are acute angles.

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