Without using trigonometric tables, evaluate the following:

$\dfrac{\text{sec 29°}}{\text{cosec 61°}} + \text{2 cot 8° cot 17° cot 45° cot 73° cot 82°} - \text{3 (sin}^2 38° + \text{sin}^2 52°)$.

Express the following in terms of trigonometric ratios of angles between 0° to 45° :

tan 81° + cos 72°

Without using trigonometric tables, prove that:

sin² 28° - cos² 62° = 0

Without using trigonometric tables, prove that:

cos² 25° + cos² 65° = 1