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

Question

asked Dec 6, 2021 23.7k views

2 Answers

Aramusss · Answer 1 · 2021-12-12T13:51:19+0000

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
and
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.