If $5x-2y-7=0$ is changed into the form $x\cos \alpha +y\sin \alpha =p$, then $\cos \alpha$ is

Given line is $5x-2y-7=0$

This line changed to normal form $5x-2y=7$

Both side divide with $\sqrt{25+4}=\sqrt{29}$

$\frac{5}{\sqrt{29}}x-\frac{2y}{\sqrt{29}}=\frac{7}{\sqrt{29}}$

This is comparing with $x\cos \alpha +y\sin \alpha =P$

$\therefore \cos \alpha =\frac{5}{\sqrt{29}}$

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