![\[\mathbf{sec}\text{ }\mathbf{\theta }\text{ }=\text{ }\mathbf{13}/\mathbf{5},\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9a2ce3144478cc2b7f9167d9e02c0f84_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given,
![\[sec\text{ }\theta \text{ }=\text{ }13/5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-048809e2df1fb61ed7b27c39d6d33b01_l3.png "Rendered by QuickLaTeX.com")
We know that,
![\[sec\text{ }\theta \text{ }=\text{ }1/\text{ }cos\text{ }\theta \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-84040a71a28f8af388f5766a631e2bc2_l3.png "Rendered by QuickLaTeX.com")
![\[\Rightarrowcos\text{ }\theta \text{ }=\text{ }1/\text{ }sec\text{ }\theta \text{ }=\text{ }1/\text{ }\left( 13/5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-460bd167063a157f26b1a77951a21088_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore cos\text{ }\theta \text{ }=\text{ }5/13\text{ }\ldots \ldots .\text{ }\left( 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c1d9239a2fe1be63d15d70c044c6fc48_l3.png "Rendered by QuickLaTeX.com")
By definition,
![\[cos\text{ }\theta \text{ }=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d4c5c998df764f2e989b6e97939d8a69_l3.png "Rendered by QuickLaTeX.com")
![\[\ldots ..\text{ }\left( 2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-197f5cce2acf811bdd00e2b0bc1265f5_l3.png "Rendered by QuickLaTeX.com")
Comparing
![\[\left( 1 \right)\text{ }and\text{ }\left( 2 \right),\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5f0fbc09a94067a6b1df1e7a7747e509_l3.png "Rendered by QuickLaTeX.com")
Adjacent side
![\[=\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e45ddd13b94c34a71f1a55ef7d8c9ef2_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }13\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c83e968add4833e03486b314c82bd63e_l3.png "Rendered by QuickLaTeX.com")
Opposite side = √((hypotenuse) 2 – (adjacent side)2)
![\[=\text{ }\surd ({{13}^{2}}~\text{ }{{5}^{2}})\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-18a234f78758b4115783a1a9acaef968_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\surd \left( 169\text{ }\text{ }25 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-de0644ea0ffd5192edee146dccddc2be_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\surd \left( 144 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e68f01e075b2133ca1c128b18f826242_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }12~~~~~~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a5f5df98b1d86aa64ec4342345f83633_l3.png "Rendered by QuickLaTeX.com")
Thus, opposite side
![\[=\text{ }12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dd99338e6f3e8f7cea5653cc0ec32a13_l3.png "Rendered by QuickLaTeX.com")
![\[tan\text{ }\theta \text{ }=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0827ee145481afbad6b4a0afab273da3_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore tan\text{ }\theta \text{ }=\text{ }12/\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9477d2938aabad03515b672bc6f63a42_l3.png "Rendered by QuickLaTeX.com")
From, let’s divide the numerator and denominator by
![\[cos\text{ }\theta .\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b6a29930f58b2b6d9c08b1c33d4d5357_l3.png "Rendered by QuickLaTeX.com")
We get,
![\[\Rightarrow \left( 2\left( 12/5 \right)\text{ }\text{ }3 \right)\text{ }/\text{ }\left( 4\left( 12/5 \right)\text{ }\text{ }9 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bfa1919b18179a6eb1090b377ba878df_l3.png "Rendered by QuickLaTeX.com")
![\[\Rightarrow \left( 24\text{ }\text{ }15 \right)\text{ }/\text{ }\left( 48\text{ }\text{ }45 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-76566c5b072fbf07b17683f7eb400437_l3.png "Rendered by QuickLaTeX.com")
![\[\Rightarrow 9/3\text{ }=\text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2110e220bc0f84e61e34e3730f21cc4c_l3.png "Rendered by QuickLaTeX.com")
![\[\therefore =\text{ }3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fdb4b033950a1fa1a2ca63f7151c1b2f_l3.png "Rendered by QuickLaTeX.com")
