Question

Find $\left[\begin{array}{cc}1& {\sin }^{2}x\\ {\cot }^{2}x& -{\sec }^{2}x\end{array}\right]+\left[\begin{array}{cc}{\tan }^{2}x& {\cos }^{2}x\\ 1& 1\end{array}\right]$

Answer 1

$\left[\begin{array}{cc}1& {\sin }^{2}x\\ {\cot }^{2}x& -{\sec }^{2}x\end{array}\right]+\left[\begin{array}{cc}{\tan }^{2}x& {\cos }^{2}x\\ 1& 1\end{array}\right]$
$=\left[\begin{array}{cc}1+{\tan }^{2}x& {\sin }^{2}x+{\cos }^{2}x\\ {\cot }^{2}x+1& 1-{\sec }^{2}x\end{array}\right]$
$=\left[\begin{array}{cc}{\sec }^{2}x& 1\\ {\text{cosec}}^{2}x& -{\tan }^{2}x\end{array}\right]$