Given:
![\[p\text{ }=\text{ }4,\text{ }\alpha \text{ }=\text{ }15{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-84ceec86607d56172eb13a50e3dc3606_l3.png "Rendered by QuickLaTeX.com")
The equation of the line in normal form is given by
as,
![\[~cos\text{ }15{}^\circ ~=\text{ }cos\text{ }\left( 45{}^\circ ~\text{ }30{}^\circ \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d7cf4d3f72274007541e8f1d5b524501_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }cos45{}^\circ cos30{}^\circ ~+\text{ }sin45{}^\circ sin30{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7424e8f74a88875cc2424074792311ea_l3.png "Rendered by QuickLaTeX.com")
And
![\[Cos\text{ }\left( A\text{ }\text{ }B \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cf0cb48712e38e7926939d4d2d8540cb_l3.png "Rendered by QuickLaTeX.com")
![\[~=\text{ }cos\text{ }A\text{ }cos\text{ }B\text{ }+\text{ }sin\text{ }A\text{ }sin\text{ }B\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-91e3e7e970ece3c9f2affa947e3cb1a6_l3.png "Rendered by QuickLaTeX.com")
Hence ,
And
![\[sin\text{ }15\text{ }=\text{ }sin\text{ }\left( 45{}^\circ ~\text{ }30{}^\circ \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f34ff8ae13d5babbee850f3a3d7f6802_l3.png "Rendered by QuickLaTeX.com")
![\[~=\text{ }sin\text{ }45{}^\circ ~cos\text{ }30{}^\circ ~\text{ }cos\text{ }45{}^\circ ~sin\text{ }30{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-16f3d899452819c28c0cc02018d38b3b_l3.png "Rendered by QuickLaTeX.com")
![\[Sin\text{ }\left( A\text{ }\text{ }B \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8c49514ef6e8450b227002621256db19_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }sin\text{ }A\text{ }cos\text{ }B\text{ }\text{ }cos\text{ }A\text{ }sin\text{ }B\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-57a9dab0191cc93c979f7d4799dd5581_l3.png "Rendered by QuickLaTeX.com")
So,
Now, on using the formula,
![\[x\text{ }cos~\alpha \text{ }+\text{ }y\text{ }sin\text{ }\alpha \text{ }=\text{ }p\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-46b724860300ac9f5afca091b543b42b_l3.png "Rendered by QuickLaTeX.com")
Now, putting the values, we have
![\[\left( \surd 3+1 \right)x\text{ }+\left( \surd 3-1 \right)\text{ }y\text{ }=\text{ }8\surd 2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-708bed60aabfcc8066328918d57a7688_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line in normal form is:
![\[~\left( \surd 3+1 \right)x\text{ }+\left( \surd 3-1 \right)\text{ }y\text{ }=\text{ }8\surd 2.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dee32bc4cc8c3bde8fc09689b0e766a3_l3.png "Rendered by QuickLaTeX.com")
