Without using trigonometrical tables, evaluate the following :

sin² 28° + sin² 62° - tan² 45°

Without using trigonometrical tables, evaluate the following :

$\dfrac{\text{2 cos 27°}}{\text{sin 63°}} + \dfrac{\text{tan 27°}}{\text{cot 63°}} + \text{cos 0°}$

Without using trigonometrical tables, evaluate the following :

5 sin 50° sec 40°- 3 cos 59° cosec 31°

Prove that :

$\dfrac{\text{cos (90° - θ) sec (90° - θ) tan θ}}{\text{cosec (90 - θ) sin (90 - θ) cot (90 - θ)}} + \dfrac{\text{tan (90 - θ)}}{\text{cot θ}} = 2.$