The number of real values of a satisfying the equation $a^{2} - 2 a s i n x + 1$ =0 is

Zero

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One

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Two

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Inifnite

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Solution

The correct option is C
Two

Given equations $a^{2} - 2 a s i n x + 1$ =0

a= $\frac{2 s i n x \pm \sqrt[2]{4 s i n^{2} x - 4}}{2}$ = sinx $\pm$ $\sqrt[2]{- (1 - s i n^{2} x)}$

a=sinx $\pm$ icosx

If x= $\frac{π}{2}$ $\Rightarrow$ a=1, x= $270^{o}$ $\Rightarrow$ a=-1.

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