Compute [ cc ^ 2 x & ^ 2 x ^ 2 x & ^ 2 x ]+ [ cc ^ 2 x & ^ 2 x ^ … - Vidyadip

Question

Compute $\left[\begin{array}{cc} {\cos ^{2} x} & {\sin ^{2} x} \\ {\sin ^{2} x} & {\cos ^{2} x} \end{array}\right]+\left[\begin{array}{cc} {\sin ^{2} x} & {\cos ^{2} x} \\ {\cos ^{2} x} & {\sin ^{2} x} \end{array}\right]$

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Answer

$\left[\begin{array}{cc} {\cos ^{2} x} & {\sin ^{2} x} \\ {\sin ^{2} x} & {\cos ^{2} x} \end{array}\right]+\left[\begin{array}{cc} {\sin ^{2} x} & {\cos ^{2} x} \\ {\cos ^{2} x} & {\sin ^{2} x} \end{array}\right]$
=$\left[\begin{array}{cc} {\cos ^{2} x+\sin ^{2} x} & {\cos ^{2} x+\sin ^{2} x} \\ {\sin ^{2} x+\cos ^{2} x} & {\cos ^{2} x+\sin ^{2} x} \end{array}\right]$
= $\left[\begin{array}{ll} {1} & {1} \\ {1} & {1} \end{array}\right]$

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