A) \[cos\text{ }\theta +i\text{ }sin\text{ }\theta \]
B) \[cos\text{ }\theta -i\text{ }sin\text{ }\theta \]
C) \[cos\text{ }\theta \pm i\text{ }sin\text{ }\theta \]
D) None of these
Correct Answer: C
Solution :
Given\[x+\frac{1}{x}=2\cos \theta \] \[\Rightarrow \] \[{{x}^{2}}-2x\cos \theta +1=0\] \[\therefore \] \[x=\frac{2\cos \theta \pm \sqrt{4co{{s}^{2}}\theta -4}}{2}\] \[=\cos \theta \pm \frac{\sqrt{-4(1-{{\cos }^{2}}\theta )}}{2}\] \[=\cos \theta \pm \frac{2i\sin \theta }{2}\] \[=\cos \theta \pm \sin \theta \]
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