Let S be the set of the possible value(s) of a such that the equationsin2(2π5x)+asin(2π5x)+sin−1(x2−10x+26)+cos−1(x2−10x+26)=0 has atleast one real solution .Then, the set S is

−1≤x2−10x+26≤1⇒x=5 only and at x = 5π2=0 which is not possible. Hence a∈o.

Let S be the set of the possible value(s) of a such that the equationsin2(2π5x)+asin(2π5x)+sin−1(x2−10x+26)+cos−1(x2−10x+26)=0 has atleast one real solution .Then, the set S is

−1≤x2−10x+26≤1⇒x=5 only and at x = 5π2=0 which is not possible. Hence a∈o.

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Let S be the set of the possible value(s) of a such that the equation $\sin^{2} (\frac{2 π}{5} x) + a \sin (\frac{2 π}{5} x) + \sin^{- 1} (x^{2} - 10 x + 26) + \cos^{- 1} (x^{2} - 10 x + 26) = 0$
has atleast one real solution .Then, the set S is

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$(- \infty, - \sqrt{2 π}] \cup [\sqrt{2 π}, \infty)$

$(- \infty, - \sqrt{2 π}] \cup [\sqrt{π}, \infty)$

$(- \sqrt{2 π}, \sqrt{2 π})$

$(- \infty, - \sqrt{2} π] \cap [\sqrt{π}, \infty)$

answer is D.

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Detailed Solution

$- 1 \leq x^{2} - 10 x + 26 \leq 1 \Rightarrow x = 5$ only and at x = 5
$\frac{π}{2} = 0$ which is not possible. Hence $a \in o$ .

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Let S be the set of the possible value(s) of a such that the equationsin2(2π5x)+asin(2π5x)+sin−1(x2−10x+26)+cos−1(x2−10x+26)=0 has atleast one real solution .Then, the set S is

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Let S be the set of the possible value(s) of a such that the equation $\sin^{2} (\frac{2 π}{5} x) + a \sin (\frac{2 π}{5} x) + \sin^{- 1} (x^{2} - 10 x + 26) + \cos^{- 1} (x^{2} - 10 x + 26) = 0$
has atleast one real solution .Then, the set S is