The value of [ ^224^ + ^266^ ^224^ + ^266^ + ^261^ + 61^ 29^ ] is equal to

Answer: Option C

$$\begin{array}{rl}& \left[\frac{{\sin }^2{24}^{\circ }+{\sin }^2{66}^{\circ }}{{\cos }^2{24}^{\circ }+{\cos }^2{66}^{\circ }}+{\sin }^2{61}^{\circ }+\cos {61}^{\circ }\sin {29}^{\circ }\right]\\ & =\frac{1}{1}+{\sin }^{2}61^{\circ }+\cos 61^{\circ }\sin \left({90}^{\circ }-{61}^{\circ }\right)\\ & =1+{\sin }^{2}61^{\circ }+{\cos }^{2}61^{\circ }\\ & =1+1\\ & =2\end{array}$$