Given trigomentry expression:
[tex]\frac{tan(-\frac{2\pi}{3})}{sin(\frac{7\pi}{4})}-sec(-\pi)[/tex]
To find the exact value,
[tex]\begin{gathered} \frac{tan(-\frac{2\pi}{3})}{sin(\frac{7\pi}{4})}-sec(-\pi) \\ use,\sec \mleft(-\pi\mright)=\frac{1}{\cos\left(-\pi\right)} \\ =\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ =-\sqrt{2}\tan (-\frac{2\pi}{3})+1 \\ =-\sqrt{2}\tan (-\frac{2\pi}{3})+1 \\ =\sqrt{2}\tan (\frac{2\pi}{3})+1 \\ =\sqrt{2}(-\sqrt{3})+1 \\ =-\sqrt{6}+1 \end{gathered}[/tex]
The answer is,
[tex]=-\sqrt[]{6}+1[/tex]
