Column-I		Column-II
A	The value of ${\left(\frac{4+\sec {20}^0}{\cos ec{20}^0}\right)}^2$ , is	P	1
B	The minimum value of   $\frac{1+\cos 2x+8{\sin }^{2}x}{2\sin 2x},x\in (0,\pi /2),$	Q	2
C	The value of  $\frac{8\sin {40}^0.\sin {50}^0.\tan {10}^0}{\cos {80}^0}$	R	3
D	If $\frac{\cos 5A}{\cos A}+\frac{\sin 5A}{\sin A}=a+b\cos 4A$ ,then $a^2/b$  is	S	4

(A) We have
 ${\left[\frac{4+\sec {20}^0}{\cos ec{20}^0}\right]}^2={\left[\frac{\sin {20}^0}{\cos {20}^0}(4\cos {20}^0+1)\right]}^2$
 $=\left[\frac{2\sin {40}^0+\sin {20}^0}{\cos {20}^0}\right]={\left[\frac{2\sin {60}^0\cos {20}^0}{\cos {20}^0}\right]}^2=3$
(B) Let  $f\left(x\right)=\frac{2{\cos }^{2}x+8{\sin }^{2}x}{2\sin 2x};f\left(x\right)>0$
 $=\frac{\cot x+4\tan x}{2}=\frac{{(\sqrt{\cot x}-2\sqrt{\tan x})}^2}{2}+2$
 $\Rightarrow \therefore f{\left(x\right)}_{\min }=2$
(C)  $\frac{8\sin {40}^0\sin {50}^0\tan {10}^0}{\cos {80}^0}$
 $=\frac{4(2\sin {50}^0.\sin {40}^0)\sin {10}^0}{\sin {10}^0.\cos {10}^0}$
 $=\frac{4(\cos {10}^0-\cos {90}^0)\sin {10}^0}{\sin {10}^0.\cos {10}^0}=4$
D) L.H.  $=\frac{2\sin 6A}{\sin 2A}=\frac{2\sin 3\left(2A\right)}{\sin 2A}$
  $=\frac{2[3\sin 2A-4{\sin }^{3}2A]}{\sin 2A}$
 $=2(3-4{\sin }^{2}2A)=2(3-2(1-\cos 4A\left)\right)$
 $=2+4\cos 4A\Rightarrow \therefore a=2,b=4\Rightarrow \therefore a^2/b=1$