If x, y∈ℝ, then the determinant ∆=cosx-sinx1sinxcosx1cosx+y-sinx – InterviewSolution

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1.	If x, y∈ℝ, then the determinant ∆=cosx-sinx1sinxcosx1cosx+y-sinx+y0 lies in the interval(a) -2, 2(b) -1, 1(c) -2, 1(d) -1, -2
Answer» If $x, y \in ℝ$ , then the determinant $∆ = \|\begin{matrix} \cos x & - \sin x & 1 \\ \sin x & \cos x & 1 \\ \cos (x + y) & - \sin (x + y) & 0 \end{matrix}\|$ lies in the interval (a) $[- \sqrt{2}, \sqrt{2}]$ (b) $[- 1, 1]$ (c) $[- \sqrt{2}, 1]$ (d) $[- 1, - \sqrt{2}]$

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