Trigonometry Question

What is the exact value of the trigonometric expression?

Hello lovesosa12!

$\color{BrickRed}\frac{tan(-\frac{7\pi}{6})}{sec(\frac{7\pi}{4})}-sin(\frac{\pi}{2}) \\ =\frac{tan(-210°)}{sec(315°)}-sin(90°)\\ =\frac{tan(-30°)}{sec(45°)}-sin(90°)\\ =\frac{-\frac{\sqrt{3}}{3}}{\sqrt{2}}-1$

$=-\frac{\sqrt{3\cdot 2}}{3}-1\\ =-(\frac{\sqrt{6}}{3}+1)$

$\Large\frac{tan(-\frac{7\pi}{6})}{sec(\frac{7\pi}{4})}-sin(\frac{\pi}{2})=-(\frac{\sqrt{6}}{3}+1)=-1.81649658$

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You are great! Thanks