Find the value of $$\frac{\sin^2{68^\circ} + \sin^2{22^\circ}}{2 \left( \cos^2{17^\circ} + \cos^2{73^\circ} \right)}$$.

Correct option is D

Given: ​

​$$\frac{\sin^2{68^\circ} + \sin^2{22^\circ}}{2 \left( \cos^2{17^\circ} + \cos^2{73^\circ} \right)}$$ 

Formula Used: ​

$$\sin(90 -\theta) = \cos \theta\\ \ \\ \cos(90 -\theta) = \sin \theta \\ \ \\ \sin^2\theta +\cos^2\theta = 1$$

Solution:

​$$\frac{\sin^2{68^\circ} + \sin^2{22^\circ}}{2 \left( \cos^2{17^\circ} + \cos^2{73^\circ} \right)}\\ \ \\ = \frac{\sin^2{68^\circ} + \sin^2{(90 -68)^\circ}}{2 \left[ \cos^2{(90-73)^\circ} + \cos^2{73^\circ} \right]} \\ \ \\ = \frac{\sin^2{68^\circ} + \cos^2{68^\circ}}{2 \left[ \sin^2{73^\circ} + \cos^2{73^\circ} \right]}\\ \ \\ = \frac{1}{2}$$​​