A) \[{{140}^{o}}\]and\[{{270}^{o}}\]
B) \[{{40}^{o}}\]and\[{{140}^{o}}\]
C) \[{{40}^{o}}\]and \[{{320}^{o}}\]
D) \[{{50}^{o}}\]and \[{{130}^{o}}\]
Correct Answer: C
Solution :
We have \[k=\cos {{20}^{o}}\] ?(i) and \[2{{k}^{2}}-1=\cos x\] ?(ii) From Eqs.(i) and (ii), we get \[2{{\cos }^{2}}{{20}^{o}}-1=\cos x\] \[\Rightarrow \] \[\cos x=\cos {{40}^{o}}\] \[\Rightarrow \] \[x={{40}^{o}}\] or \[x={{360}^{o}}-{{40}^{o}}={{320}^{o}}\] \[\therefore \] The values of \[x\]lying between\[{{0}^{o}}\] and \[{{360}^{o}}\] are \[{{40}^{o}}\] and \[{{320}^{o}}.\]
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