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If $3 π / 4 < α < π,$ then the set of values of $α$ for which $(\sin α) x^{2} + (2 \cos α) x + \frac{1}{2} (\sin α + \cos α)$ is square of a linear polynomial is

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$\{\frac{5 π}{6}\}$

$\{\frac{5 π}{6}, \frac{11 π}{12}\}$

$\{\frac{11 π}{12}\}$

$ϕ$

answer is D.

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Detailed Solution

$4 \cos^{2} α - 2 \sin α (\sin α + \cos α) = 0 \Rightarrow 1 + 3 \cos 2 α = \sin 2 α$

For $3 π / 4 < α < π,$ left side is positive and right side is negative.

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