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Statement-1: 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 in the interval (0, π/2). Statement-2: The equation in α | cos α sin α cos α | | sin α cos α sin α | = 0 | cos α sin α − cos α | has only one solution lying in the interval (0, π/2)

1. Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-1.
2. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
3. Statement-1 is true, Statement-2 is false.
4. Statement-1 is false, Statement-2 is true.

Correct answer: Statement-1 is true, Statement-2 is false.

Solution

Statement-1 is true because the determinant of the coefficient matrix must be zero for a non-trivial solution, which occurs for a specific value of α. However, Statement-2 is false because the determinant equation does not yield a unique solution in the specified interval, contradicting the claim.

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