Proving equations, (Discrete maths)

[karan000]

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?

 

[epenguin]

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.

 

[Infrared]

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.

 

[Dick]

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.