Question

If $f\left(x\right)=\left[\begin{array}{ccc}\cos x& -\sin x& 0\\ \sin x& \cos x& 0\\ 0& 0& 1\end{array}\right]$, then $f(x+y)$ is equal to:

• A. $f\left(x\right)+f\left(y\right)$
• B. $f\left(x\right)-f\left(y\right)$
• C. $f\left(x\right).f\left(y\right)$
• D. None of these

Answer 1

The correct option is C $f\left(x\right).f\left(y\right)$

Expanfing along $c_3,f\left(n\right)=co{s}^{2}x+si{n}^{2}x=1$

$\Rightarrow f(x+y)=1,f\left(y\right)=1$

$\Rightarrow f(x+y)=f\left(n\right)f\left(y\right)$ is true only

$\Rightarrow \left(c\right)$