Answer:
Steps 2 and 3 must be switched.
Step-by-step explanation:
Let [tex]\tan \left(\frac{3\pi}{4}-B \right)[/tex]. From Trigonometry we know the following identity:
[tex]\tan (a-b) = \frac{\tan a -\tan b}{1+\tan a\cdot \tan b}[/tex] (Eq. 1)
Where [tex]a[/tex] and [tex]b[/tex] are angles measured in radians.
Now we proceed to demonstrate the required steps to expand and simplify given expression:
1) [tex]\tan \left(\frac{3\pi}{4}-B \right)[/tex] Given.
2) [tex]\frac{\tan \frac{3\pi}{4}-\tan B }{1+\tan \frac{3\pi}{4}\cdot \tan B }[/tex] [tex]\tan (a-b) = \frac{\tan a -\tan b}{1+\tan a\cdot \tan b}[/tex] (Step 1)
3) [tex]\frac{-1-\tan B}{1+(-1)\cdot \tan B}[/tex] Trigonometric identity. (Step 3)
4) [tex]\frac{(-1)\cdot (1+\tan B)}{1-\tan B}[/tex] Distributive property/[tex](-1)\cdot a = -a[/tex] (Step 2)
5) [tex]-\frac{1+\tan B}{1-\tan B}[/tex] [tex](-1)\cdot a = -a[/tex]/[tex]\frac{-a}{b} = -\frac{a}{b}[/tex]/Result. (Step 4)
In a nutshell, steps 2 and 3 must be switched.
