A) \[5/\sqrt{13}\]
B) \[5/\sqrt{26}\]
C) \[5/13\]
D) \[5/26\]
E) None of these
Correct Answer: E
Solution :
Given, \[\tan x=\frac{5}{12}\] and x is in II quadrant. \[\therefore \] \[\sin x=\frac{-5}{13}\] and \[\cos x=\frac{-12}{13}\] Now, \[\cos x=2{{\cos }^{2}}\frac{x}{2}-1\] \[\Rightarrow \] \[{{\cos }^{2}}\frac{x}{2}=\frac{1}{2}(\cos x+1)\] \[=\frac{1}{2}\left( \frac{-12}{13}+1 \right)\] \[=\frac{1}{2}\left( \frac{1}{13} \right)=\frac{1}{26}\,\,\Rightarrow \cos \frac{x}{2}=\sqrt{\frac{1}{26}}\]You need to login to perform this action.
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