Question bank/JEE Main/Mathematics

Let $\lambda$ and $\alpha$ be real. If denote the set
of all values of $\lambda$ for which the system of linear equations
$\lambda x + (sin\lambda)y + (cos\alpha)z = 0$
$x + (cos\alpha)y + (sin\alpha)z = 0$
$- x + (sin\alpha)y - (cos\alpha)z = 0$
has a non-trivial solution, then a+b+1 is

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For non-trivial solution [IMAGE] Expanding along $C_{1},$ we get
$\lambda = sin2\alpha + cos2\alpha$
$\therefore - \sqrt{2} \leq \lambda \leq \sqrt{2}$

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx