NCERT Sol Maths Class XII Ch-3 | Matrices
Solution of Important Question of NCERT Book Class XII Chapter 3 Matrices Get Free NCERT Solutions for Class 12 Maths Chapter 3 Matrices. Solution of important questions of NCERT book solved by Expert Teachers as per NCERT (CBSE) Book guidelines. NCERT Exercise 3.2 Q.18: If I is an identity matrix of order 2 x 2 then show that \[I+A=I-A\begin{bmatrix} cos\alpha &-sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix}\; \; where\] \[A=\begin{bmatrix} 0 &-tan\frac{\alpha }{2} \\ tan\frac{\alpha }{2}& 0 \end{bmatrix}\] Solution \[Let\; \; tan\frac{\alpha }{2}=t\]\[Then\; \; A=\begin{bmatrix} 0 &-t \\ t&0 \end{bmatrix}\] \[LHS= I+A=\begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix}+\begin{bmatrix} 0 &-t \\ t&0 \end{bmatrix}=\begin{bmatrix} 1 &-t \\ t & 1 \end{bmatrix}\] \[Now:\; \; cos\alpha =\frac{1-tan^{2}\frac{\alpha }{2}}{1+tan^{2}\frac{\alpha }{2}}=\frac{1-t^{2}}{1+t^{2}}\;\; and\] \[sin\alpha =\frac{2tan^{2}\frac{\alpha }{2}}{1+tan...