List I has four entries and List II has five entries. Each entry of List I is to be correctly matched with one or more than one entries of List II. List IList II (P)⎛⎝1y2(cos(tan−1y)+ysin(tan−1y)2cot(sin−1y)+tan(sin−1y))2+y4⎞⎠1/2(1)12√53takes value (Q)Ifcosx+cosy+cosz=0=sinx+siny+sinz(2)√2then possible value of cosx−y2is(R)Ifcos(π4−x)cos2x+sinxsin2xsecx(3)12=cosxsin2xsecx+cos(π4+x)cos2xthen possible value ofsecx is(S)Ifcot(sin−1√1−x2)=sintan−1(x√6)),x≠0(4)1then possible value of x isWhich of the following is the only CORRECT combination?

List I has four entries and List II has five entries. Each entry of Li

1.	List I has four entries and List II has five entries. Each entry of List I is to be correctly matched with one or more than one entries of List II. List IList II (P)⎛⎝1y2(cos(tan−1y)+ysin(tan−1y)2cot(sin−1y)+tan(sin−1y))2+y4⎞⎠1/2(1)12√53takes value (Q)Ifcosx+cosy+cosz=0=sinx+siny+sinz(2)√2then possible value of cosx−y2is(R)Ifcos(π4−x)cos2x+sinxsin2xsecx(3)12=cosxsin2xsecx+cos(π4+x)cos2xthen possible value ofsecx is(S)Ifcot(sin−1√1−x2)=sintan−1(x√6)),x≠0(4)1then possible value of x isWhich of the following is the only CORRECT combination?
Answer» $List I$ has four entries and $List II$ has five entries. Each entry of $List I$ is to be correctly matched with one or more than one entries of $List II .$ $\begin{matrix} List I & List II (P) & {⎛ ⎝ \frac{1}{y^{2}} {(\frac{cos ({tan}^{- 1} y) + y sin ({tan}^{- 1} y)^{2}}{cot ({sin}^{- 1} y) + tan ({sin}^{- 1} y)})}^{2} + y^{4} ⎞ ⎠}^{1 / 2} & (1) & \frac{1}{2} \sqrt{\frac{5}{3}} takes value (Q) & If cos x + cos y + cos z = 0 = sin x + sin y + sin z & (2) & \sqrt{2} then possible value of cos \frac{x - y}{2} is (R) & If cos (\frac{π}{4} - x) cos 2 x + sin x sin 2 x sec x & (3) & \frac{1}{2} = cos x sin 2 x sec x + cos (\frac{π}{4} + x) cos 2 x then possible value of sec x is (S) & If cot ({sin}^{- 1} \sqrt{1 - x^{2}}) = sin {tan}^{- 1} (x \sqrt{6})), x \neq 0 & (4) & 1 then possible value of x is \end{matrix}$ Which of the following is the only CORRECT combination?