Statement I: The system of linear equations
$x + (\sin α) y + (\cos α) z = 0$
$x + (\cos α) y + (\sin α) z = 0$
$- x + (\sin α) y - (\cos α) z = 0$
Has a non trivial solution for only one value of $α$ lying between $0$ and $π .$
Statement II: $| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{matrix} | = 0$
has no solution in the interval $- \frac{π}{4} < x < \frac{π}{4} .$

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Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement II

Statement I is true, Statement II is false

Statement I is false, Statement II is true

Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

answer is B.

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Detailed Solution

In statement, $| \begin{matrix} 1 & \sin α & \cos α \\ 1 & \cos α & \sin α \\ - 1 & \sin α & - \cos α \end{matrix} | = 0 \Rightarrow$ Either $\sin α = 0$ or $\tan α = 1 \Rightarrow α = π / 4 (a s 0 < α < π)$

And Statement II, $(\sin x + 2 \cos x)$

$| \begin{matrix} 1 & \cos x & \cos α \\ 1 & \sin x & \cos x \\ 1 & \cos x & \sin x \end{matrix} | = 0 \Rightarrow (\sin x + 2 \cos x) {(\cos x - \sin x)}^{2} = 0$