The value of 23^ 67^ + 52^ 38^ + 23^ 67^ + cosec\,52^ 38^ cose c^2\,20^ - ^270^ is:

Answer: Option A

$$\begin{array}{rl}& \frac{\sin {23}^{\circ }\cos {67}^{\circ }+\sec {52}^{\circ }\sin {38}^{\circ }+\cos {23}^{\circ }\sin {67}^{\circ }+\text{cosec}{52}^{\circ }\cos {38}^{\circ }}{\text{cose}{\text{c}}^2{20}^{\circ }-{\tan }^2{70}^{\circ }}\\ & =\frac{{\sin }^2{23}^{\circ }+\frac{1}{\cos {52}^{\circ }}\times \cos {52}^{\circ }+{\cos }^2{23}^{\circ }+\frac{1}{\sin {52}^{\circ }}\times \sin {52}^{\circ }}{\text{cose}{\text{c}}^2{20}^{\circ }-{\cot }^2{20}^{\circ }}\\ & =\frac{{\sin }^2{23}^{\circ }+1+{\cos }^2{23}^{\circ }+1}{1}\left[\therefore {\sin }^2\theta +{\cos }^2\theta =1\right]\\ & =1+1+1\\ & =3\end{array}$$