Match the following.

List - I	List - II
$1) \cos {20}^{\circ }+\cos {140}^{\circ }+\cos {100}^{\circ }=$	$\mathrm{a}) 0$
$2) (1+\tan {20}^{\circ }\left)\right(1+\tan {25}^{\circ })=$	$\mathrm{b}) 2$
$3) \tan {20}^{\circ }\tan {32}^{\circ }+\tan {32}^{\circ } \tan {38}^{\circ } +\tan {38}^{\circ }\tan {20}^{\circ }=$	$\mathrm{c}) 1$
$4) {\sin }^2{10}^0+{\sin }^2{110}^0+{\sin }^2{130}^0=$	$\mathrm{d}) \frac{3}{2}$

 $\begin{array}{rcl}1)& & \cos {20}^{\circ }+\cos {140}^{\circ }+\cos {100}^{\circ }\\ & =& \cos {20}^{\circ }+\cos ({120}^{\circ }+{20}^{\circ }) +\cos ({120}^{\circ }-{20}^{\circ })\\ & =& \cos {20}^{\circ }+2\cos {120}^{\circ } \cos {20}^{\circ }\\ & =& \cos {20}^{\circ }-\cos {20}^{\circ }=0\end{array}$
 $\begin{array}{lcl}2) (1+\tan {20}^{\circ }) (1+\tan {25}^{\circ })& & \\ \mathrm{A}+\mathrm{B}\begin{array}{cl}=& {45}^{\circ }\end{array}& & \\ (1+\tan \mathrm{A}) (1+\tan \mathrm{B})\begin{array}{cl}=& 2\end{array}& & \\ (1+\tan {20}^{\circ }) (1+\tan {25}^{\circ })& =& 2\end{array}$ 

 $\begin{array}{lcl}3) \tan {20}^{\circ } \tan {32}^{\circ }+\tan {32}^{\circ } \tan {38}^{\circ }+\tan {38}^{\circ } \tan {20}^{\circ }& & \\ \mathrm{A}+\mathrm{B}+\mathrm{C}={90}^o& & \\ \tan \mathrm{A} \tan \mathrm{B}+\tan \mathrm{B} \tan \mathrm{C}+\tan \mathrm{C} \tan \mathrm{A}=1& & \end{array}$

 $\begin{array}{rcl}4)& {\sin }^2{10}^{\circ }+{\sin }^2{110}^{\circ }+{\sin }^2{130}^{\circ }& \\ & =\begin{array}{l}=1+{\sin }^2{10}^{\circ }-({\cos }^2{130}^{\circ }-{\sin }^2{110}^{\circ })\\ 1+\frac{1-\cos {20}^{\circ }}{2}-\cos {120}^{\circ } \cos 20\\ 1+\frac{1}{2}-\frac{1}{2}\cos 20+\frac{1}{2}\cos {20}^{\circ }=\frac{3}{2}\end{array}& \\ & & \\ & & \end{array}$