Question

How must the proof be rearranged for the steps to logically follow each other?

Answer 1

C

Explanation:

EDGE 2020

Answer 2

Steps 2 and 3 must be switched.

Explanation:

Let
`\tan \left((3\pi)/(4)-B \right)`. From Trigonometry we know the following identity:

`\tan (a-b) = (\tan a -\tan b)/(1+\tan a\cdot \tan b)` (Eq. 1)

Where
`a` and
`b` are angles measured in radians.

Now we proceed to demonstrate the required steps to expand and simplify given expression:

1)
`\tan \left((3\pi)/(4)-B \right)` Given.

2)
`(\tan (3\pi)/(4)-\tan B )/(1+\tan (3\pi)/(4)\cdot \tan B )`
`\tan (a-b) = (\tan a -\tan b)/(1+\tan a\cdot \tan b)` (Step 1)

3)
`(-1-\tan B)/(1+(-1)\cdot \tan B)` Trigonometric identity. (Step 3)

4)
`((-1)\cdot (1+\tan B))/(1-\tan B)` Distributive property/
`(-1)\cdot a = -a` (Step 2)

5)
`-(1+\tan B)/(1-\tan B)`
`(-1)\cdot a = -a`/
`(-a)/(b) = -(a)/(b)`/Result. (Step 4)

In a nutshell, steps 2 and 3 must be switched.