# Mathematical induction for differentiationWatch

#1
Use mathematical induction to prove that for all positive integers n,

= n

So to start off,

Let P(n) be = n

Basis case, when n=1,

Suppose n=k,

=

=

Can anyone help me go from here? I'm nt sure how to clear off the k's in the angle right now...
0
11 years ago
#2
=

=

Can anyone help me go from here? I'm nt sure how to clear off the k's in the angle right now...
Instead of expanding , just use the chain rule.
0
11 years ago
#3
Yeah and remember sinx and cosx are the same graph just a translation apart.
0
#4
(Original post by insparato)
Yeah and remember sinx and cosx are the same graph just a translation apart.
What does this mean?
0
11 years ago
#5
(Original post by andrewlee89)
What does this mean?
cos x = sin(x+a) for a suitable choice of a.
0
#6
Oh.. Well that's true but this is proof by induction I need to get the whole equation into the k+1 format for proof
0
11 years ago
#7
(Original post by andrewlee89)
Oh.. Well that's true but this is proof by induction I need to get the whole equation into the k+1 format for proof
Yes, we know it's proof by induction. How do you think you are going to go from to ? Do you think it might possibly be by adding at some point?
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#8
(Original post by DFranklin)
Yes, we know it's proof by induction. How do you think you are going to go from to ? Do you think it might possibly be by adding at some point?
True :P Thx for the help. Will continue at it.
0
11 years ago
#9
u got it yet?

cos x = sin (x+pi/2) or sin x = cos (x-pi/2) is the thing u need. it is actually a very short proof
0
#10
u got it yet?

cos x = sin (x+pi/2) or sin x = cos (x-pi/2) is the thing u need. it is actually a very short proof
Got it thx guys. U all rock. At various different times lol
0
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