Match List $I$ with List $II$ and select the correct answer using the code given below the lists: List $IP.\,\,\,\,\,$ $${\left( {{1 \over {{y^2}}}{{\left( {{{\cos \left( {{{\tan }^{ - 1}}y} \right) + y\sin \left( {{{\tan }^{ - 1}}y} \right)} \over {\cot \left( {{{\sin }^{ - 1}}y} \right) + \tan \left( {{{\sin }^{ - 1}}y} \right)}}} \right)}^2} + {y^4}} \right)^{1/2}}$$ takes value $Q.\,\,\,\,$ If $$\cos x + \cos y + \cos z = 0 = \sin x + \sin y + \sin z$$ then possible value of $\cos {{x - y} \over 2}$ is $R.\,\,\,\,\,$ If $$\cos \left( {{\pi \over 4} - x} \right)\cos 2x + \sin x\sin 2\sec x = \cos x\sin 2x\sec x + \cos \left( {{\pi \over 4} + x} \right)\cos 2x$$ then possible value of $\sec x$ is $S.\,\,\,\,\,$ If $$\cot \left( {{{\sin }^{ - 1}}\sqrt {1 - {x^2}} } \right) = \sin \left( {{{\tan }^{ - 1}}\left( {x\sqrt 6 } \right)} \right),\,\,x e 0,$$ Then possible value of $x$ is List $II1.\,\,\,\,\,{1 \over 2}\sqrt {{5 \over 3}} 2.\,\,\,\,\,\sqrt 2 3.\,\,\,\,\,{1 \over 2}1.\,\,\,\,1$