Proving equations, (Discrete maths)

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The discussion focuses on a student's struggle to prove specific equations related to tangent functions in discrete mathematics. They have successfully completed a summation but are stuck on proving the equations involving tan(k) and tan(k-1). Suggestions include starting with the more complex side of the equation and simplifying it, as well as applying a general formula for the product of tangent functions. Additionally, recognizing the third part of the problem as a telescoping series may simplify the process. Overall, the conversation emphasizes strategic approaches to tackling mathematical proofs.
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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?
 
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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.
 
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A general rule for proving trig equations is to start with the more complicated side and simplify. Start with

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

by using your formula for tan(k-1)

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 tan(k)tan(k-1) 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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