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If x be real, show that cos theta cannot...

If `x` be real, show that `cos theta` cannot be equal to `x+(1)/(x)`.

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If possible, let .cos theta=x+(1)/(x) rarr cos theta=(x^(2)+1)/(x).
.rarr x^(2)-x cos theta+1=0 rarr x=(cos theta pm sqrt(cos ^(2) theta-4))/(2).
Since .x. is real, we have .cos ^(2) theta-4 geq 0., ie, .cos ^(2) theta geq 4., which is impossible, because .cos ^(2) theta le 1.
.therefore cos theta. cannot be.equal to .x+(1)/(x).
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