Proving equations, (Discrete maths)

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Homework Help Overview

The discussion revolves around proving equations related to trigonometric identities within the context of discrete mathematics, specifically focusing on the tangent function. Participants are engaged in exploring methods to approach the proof of these equations as part of their exam preparation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various strategies for proving the equations, including expanding the tangent function and manipulating terms. There are mentions of starting with more complex sides of the equations and simplifying, as well as suggestions to consider specific cases of the tangent function.

Discussion Status

The discussion is ongoing, with participants sharing different approaches and insights. Some guidance has been offered regarding how to manipulate the equations, but there is no explicit consensus on a single method or solution path. The original poster expresses frustration with their current attempts, indicating a need for further clarification.

Contextual Notes

Participants are preparing for an exam and are at an early stage in their study of discrete mathematics. There is a mention of successfully completing a summation, which may indicate varying levels of understanding among participants regarding different aspects of the material.

karan000
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Homework Statement


http://puu.sh/2mrWM

I'm practicing for my upcoming exam on discrete mathematics (we're not really too far in yet), and I cannot no matter how hard I try prove the equations. I expand tan(k-1) and then multiply by tan(k) and always end up at a dead end, it is driving me crazy.

I did however manage to do the summation without any problems...

So can someone please shed some light as to the approach I need to take to complete the first part of the question?
 
Last edited by a moderator:
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karan000 said:

Homework Statement


http://puu.sh/2mrWM

I'm practicing for my upcoming exam on discrete mathematics (we're not really too far in yet), and I cannot no matter how hard I try prove the equations. I expand tan(k-1) and then multiply by tan(k) and always end up at a dead end, it is driving me crazy.

I did however manage to do the summation without any problems...

So can someone please shed some light as to the approach I need to take to complete the first part of the question?

You are looking for product of 2 particular tans in 2nd. eq.

The first eq on RHS has a product of 2 general tans.
Shuffle it about , obtain formula for product of 2 general tans.
Apply to particular case.
 
Last edited by a moderator:
A general rule for proving trig equations is to start with the more complicated side and simplify. Start with

[itex]{\frac{\tan(k)-tan(k-1)}{tan(1)}} -1[/itex] and show that it is equal to what you get after expanding [itex]tan(k)tan(k-1)[/itex]

by using your formula for [itex]tan(k-1)[/itex]

While this might not be the direction your instructor wants, the steps of the proof will be much more natural and since all the steps you do will be reversible it will be easy to make your proof more 'correct by starting with [itex]tan(k)tan(k-1)[/itex] and ending at the desired result.

The third part of your problem is easy if you recognize it as a telescoping series.
 
karan000 said:
I'm practicing for my upcoming exam on discrete mathematics (we're not really too far in yet), and I cannot no matter how hard I try prove the equations. I expand tan(k-1) and then multiply by tan(k) and always end up at a dead end, it is driving me crazy.

I did however manage to do the summation without any problems...

So can someone please shed some light as to the approach I need to take to complete the first part of the question?

Just put A=k and B=k-1.
 

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