# Class 12 Mathematics Determinants: NCERT Solutions for Question 2

This page focuses on the detailed Determinants question answers for Class 12 Mathematics Determinants, addressing the question: 'Evaluate the determinants (i) \begin{vmatrix} \mathbf{Cosθ} & \mathbf{−sin θ} \\ \mathbf{sin θ} & \mathbf{cos θ} \end{vmatrix}(ii) \begin{vmatrix} \mathbf{x^2 − x + 1} & \mathbf{x − 1} \\ \mathbf{x + 1} & \mathbf{x + 1} \end{vmatrix}'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 2

## Evaluate the determinants (i) \begin{vmatrix} \mathbf{Cosθ} & \mathbf{−sin θ} \\ \mathbf{sin θ} & \mathbf{cos θ} \end{vmatrix}(ii) \begin{vmatrix} \mathbf{x^2 − x + 1} & \mathbf{x − 1} \\ \mathbf{x + 1} & \mathbf{x + 1} \end{vmatrix}

(i) \begin{vmatrix} \mathbf{Cosθ} & \mathbf{−sin θ} \\ \mathbf{sin θ} &  \mathbf{cos θ} \end{vmatrix}

= (cos θ)(cos θ) − (−sin θ)(sin θ)

= cos2 θ+ sin2 θ

= 1

(ii) \begin{vmatrix} \mathbf{x^2 − x + 1} & \mathbf{x − 1} \\ \mathbf{x + 1} &  \mathbf{x + 1} \end{vmatrix}

= (x2x + 1)(x + 1) − (x − 1)(x + 1)

= x3x2 + x + x2x + 1 − (x2 − 1)

= x3 + 1 − x2 + 1

= x3x2 + 2