Skip to main content
Back to Matrices & Determinants
JEE Main 2019
Matrices & Determinants
Matrices and Determinants
Medium

Question

The number of distinct real roots of \left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right| = 0 in the interval −π4≤x≤π4 - {\pi \over 4} \le x \le {\pi \over 4} is :

Options

Solution

Key Concepts Used:

  1. Properties of Determinants:
    • Applying elementary row/column operations (Ri→Ri+kRjR_i \to R_i + k R_j or Ci→Ci+kCjC_i \to C_i + k C_j) does not change the value of the determinant.
    • If a row or column has a common factor, it can be taken out of the determinant.
    • A determinant can be expanded along any row or column.
  2. Solving Trigonometric Equations: Finding values of xx that satisfy equations involving trigonometric functions.
  3. Range of Trigonometric Functions: Understanding the possible values a trigonometric function can take within a specified interval.

**Step-by-Step Solution

Previous QuestionNext Question

Practice More Matrices & Determinants Questions

View All Questions