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

How must the proof be rearranged for the steps to logically follow each other?-example-1
User Jannis M
by
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2 Answers

6 votes

Answer:

C

Explanation:

EDGE 2020

User Melc
by
8.2k points
1 vote

Answer:

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.

User Aramusss
by
8.0k points

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