This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given matrix R_. The matrix R_ is given as: R_ = & - \\ & Step 2: Calculate the determinant of R_, denoted as (R_). For a 2 × 2 matrix a & b \\ c & d , the determinant is calculated as ad - bc. Here, a = , b = -, c = , d = . Applying this formula to matrix R_: (R_) = ()() - (-)() (R_) = ^2 - (-^2) (R_) = ^2 + ^2 Step 3: Apply the fundamental trigonometric identity. The fundamental trigonometric identity states that ^2 + ^2 = 1. Therefore: (R_) = 1 Step 4: Compare the result with the given options. The calculated determinant is 1. This matches option D. The final answer is D. 1.