Question

Need help solving this, having trouble with it. Please show your own work so I can have a better understanding of itThis is a practice from my ACT prep guide

Answer 1

Given trigomentry expression:

`(tan(-(2\pi)/(3)))/(sin((7\pi)/(4)))-sec(-\pi)`

To find the exact value,

`\begin{gathered} (tan(-(2\pi)/(3)))/(sin((7\pi)/(4)))-sec(-\pi) \\ use,\sec \mleft(-\pi\mright)=(1)/(\cos\left(-\pi\right)) \\ =(\tan(-(2\pi)/(3)))/(\sin((7\pi)/(4)))-(1)/(\cos(-\pi)) \\ =-√(2)\tan (-(2\pi)/(3))+1 \\ =-√(2)\tan (-(2\pi)/(3))+1 \\ =√(2)\tan ((2\pi)/(3))+1 \\ =√(2)(-√(3))+1 \\ =-√(6)+1 \end{gathered}`

The answer is,

`=-\sqrt[]{6}+1`