Question

If $ x+\frac{1}{x}=2\cos \theta , $ then $ x $ is equal to

• 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

Answer 1

Answer: (C)

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 $