Question

review the steps of the proof. $\tan(\frac{3pi}{4}-\theta)$
step 1: $\frac{\tan(\frac{3pi}{4})-\tan\theta}{1 + \tan(\frac{3pi}{4})\tan\theta}$
step 2: $\frac{- 1-\tan\theta}{1+\tan\theta}$
step 3: $\frac{- (1 + \tan\theta)}{1+\tan\theta}$
step 4: $-1$
how must the proof be rearranged for the steps to logically follow each other?
○ step 2 should be the last step.
○ step 3 should be the last step.
○ steps 2 and 3 must be switched.
○ steps 3 and 4 must be switched.

Explanation:

Step1: Analyze step 1

Uses tangent - difference formula $\tan(A - B)=\frac{\tan A-\tan B}{1 + \tan A\tan B}$ with $A=\frac{3\pi}{4}$ and $B = \theta$.

Step2: Evaluate step 2

Simplifies $\tan(\frac{3\pi}{4})=- 1$ in the formula from step 1. But the current step 3 is a further simplification of step 2's result.

Step3: Determine correct order

So steps 2 and 3 must be switched for logical flow.

Answer:

Steps 2 and 3 must be switched.