Solution:
we have been asked to find the exact value of [tex] sec\frac{7 \pi}{6} [/tex]
This is atrigonometric ratio as we know the values of trigonmetric ratios can be found using calculator or from the trionometric ratios table.
So here we can re-write it as below:
[tex] sec\frac{7 \pi}{6} =sec( \pi +\frac{ \pi}{6} )\\
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\text{This can be further written using }sec(\pi+x)=-secx \\
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sec\frac{7 \pi}{6} =-sec( \frac{ \pi}{6} )\\
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sec\frac{7 \pi}{6} =-sec( \frac{ \pi}{6} )=- \frac{2}{\sqrt{3}}\\ [/tex]
