MCQ
જો $\frac{1}{x} + x = 2\cos \theta ,$ તો ${x^n} + \frac{1}{{{x^n}}}$ = . . .
- ✓$2\cos n\theta $
- B$2\sin n\theta $
- C$\cos n\,\theta $
- D$\sin \,n\theta $
==>$x = \cos \theta \pm i\sin \theta $
==> ${x^n} = \cos n\theta \pm i\sin n\theta $
==>$\frac{1}{x} = \frac{1}{{\cos \theta \pm i\sin \theta }}$
==> $\frac{1}{x} = \cos \theta \mp i\sin \theta $
==>$\frac{1}{{{x^n}}} = \cos n\theta \mp i\sin n\theta $
Thus, ${x^n} + \frac{1}{{{x^n}}} = 2\cos n\theta $.
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