It is given that
![\[tan\text{ }x\text{ }=\text{ }\text{ }5/12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-130d02072d9d0f5a0289ab79fcbaa4d3_l3.png "Rendered by QuickLaTeX.com")
We can compose it as
We realize that
![\[1\text{ }+\text{ }tan2\text{ }x\text{ }=\text{ }sec2\text{ }x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c7c0aec1a35e20b8e03b72f163303c54_l3.png "Rendered by QuickLaTeX.com")
We can compose it as
![\[1\text{ }+\text{ }\left( -\text{ }5/12 \right)2\text{ }=\text{ }sec2\text{ }x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f7c5df0abe7670ce10b24ade16ec8eff_l3.png "Rendered by QuickLaTeX.com")
Subbing the qualities
![\[1\text{ }+\text{ }25/144\text{ }=\text{ }sec2\text{ }x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-65704a8d391397bf3d42a576e9499fde_l3.png "Rendered by QuickLaTeX.com")
![\[sec2\text{ }x\text{ }=\text{ }169/144\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-13866b11685d57686a161bf6e79a2483_l3.png "Rendered by QuickLaTeX.com")
![\[sec\text{ }x\text{ }=\text{ }\pm \text{ }13/12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1288aecb4b48549ba7f1ecb0325084e7_l3.png "Rendered by QuickLaTeX.com")
Here x lies in the second quadrant so the worth of sec x will be negative
![\[sec\text{ }x\text{ }=\text{ }\text{ }13/12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-168b12b624a4d6fa2a3a23d901530674_l3.png "Rendered by QuickLaTeX.com")
We can compose it as
Find the values of other five trigonometric functions tan x = -5/12, x lies in second quadrant
Find the values of other five trigonometric functions tan x = -5/12, x lies in second quadrant