Evaluate the following :

$\dfrac{\text{sin}^2 22° + \text{sin}^2 68°}{\text{cos}^2 22° + \text{cos}^2 68°}$ + sin² 63° + cos 63° sin 27°

Since, angles are acute in the equation,

∴ cos(90° - θ) = sin θ, sin(90° - θ) = cos θ.

Using above equations in

$\dfrac{\text{sin}^2 22° + \text{sin}^2 68°}{\text{cos}^2 22° + \text{cos}^2 68°}$ + sin² 63° + cos 63° sin 27°

= $\dfrac{\text{sin}^2 22° + \text{sin}^2 (90 - 22)°}{\text{cos}^2 22° + \text{cos}^2 (90 - 22)°}$ + sin² 63° +cos 63° sin (90 - 63)°

= $\dfrac{\text{sin}^2 22° + \text{cos}^2 22°}{\text{cos}^2 22° + \text{sin}^2 22°}$ + sin² 63° + cos 63° cos 63°

= $\dfrac{1}{1}$ + sin² 63° + cos² 63°

= 1 + 1

= 2.

Hence, the value of expression is 2.