The number of real values of a satisfying the equation $a^2-2a sinx+1=0$ is

Zero

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One

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Two

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Infinite

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Solution

The correct option is C Two
Given equation $a^{2} - 2 a s i n x + 1 = 0 ∴ a = \frac{2 s i n x \pm \sqrt{4 s i n^{2} x - 4}}{2} = s i n x \pm \sqrt{- (1 - s i n^{2} x)} a = s i n x \pm i c o s x i f x = \frac{π}{2} \Rightarrow a = 1, x = 270^{\circ} \Rightarrow a = - 1.$

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