NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 18

✅ Step-by-Step Solution

1. Write u=tan(α/2). Use sin α=2u/(1+u²), cos α=(1−u²)/(1+u²).
2. Multiplication gives (I−A)R=\(\left[\begin{matrix}\sin{\left(\alpha \right)} \tan{\left(\frac{\alpha}{2} \right)} + \cos{\left(\alpha \right)} & - \sin{\left(\alpha \right)} + \cos{\left(\alpha \right)} \tan{\left(\frac{\alpha}{2} \right)}\\\sin{\left(\alpha \right)} - \cos{\left(\alpha \right)} \tan{\left(\frac{\alpha}{2} \right)} & \sin{\left(\alpha \right)} \tan{\left(\frac{\alpha}{2} \right)} + \cos{\left(\alpha \right)}\end{matrix}\right]\).
3. The diagonal terms cos α+u sin α simplify to 1. The top-right term −sin α+u cos α simplifies to −u, and the bottom-left is u.
4. Thus the product is \(\left[\begin{matrix}1 & - \tan{\left(\frac{\alpha}{2} \right)}\\\tan{\left(\frac{\alpha}{2} \right)} & 1\end{matrix}\right]\)=I+A.