Proving the Reduction Formula of $tan^n(theta)$
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The following is what I have tried to prove the reduction formula of $tan^n(theta)$.
For the last step, how to convert the $int sec^2(theta) tan^{n-1}(theta)dtheta $ to $frac {tan^{n-1}theta}{n-1}$?
Thank you for your help.
calculus reduction-formula
edited Jan 6 at 23:08
clathratus
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
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add a comment |
$begingroup$
The following is what I have tried to prove the reduction formula of $tan^n(theta)$.
For the last step, how to convert the $int sec^2(theta) tan^{n-1}(theta)dtheta $ to $frac {tan^{n-1}theta}{n-1}$?
Thank you for your help.
calculus reduction-formula
edited Jan 6 at 23:08
clathratus
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
$endgroup$
$begingroup$
sosmath.com/CBB/viewtopic.php?p=47786
$endgroup$
– lab bhattacharjee
May 13 '14 at 13:03
add a comment |
$begingroup$
The following is what I have tried to prove the reduction formula of $tan^n(theta)$.
For the last step, how to convert the $int sec^2(theta) tan^{n-1}(theta)dtheta $ to $frac {tan^{n-1}theta}{n-1}$?
Thank you for your help.
calculus reduction-formula
edited Jan 6 at 23:08
clathratus
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
$endgroup$
The following is what I have tried to prove the reduction formula of $tan^n(theta)$.
For the last step, how to convert the $int sec^2(theta) tan^{n-1}(theta)dtheta $ to $frac {tan^{n-1}theta}{n-1}$?
Thank you for your help.
calculus reduction-formula
calculus reduction-formula
edited Jan 6 at 23:08
clathratus
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
edited Jan 6 at 23:08
clathratus
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
edited Jan 6 at 23:08
clathratus
5,1141439
edited Jan 6 at 23:08
clathratus
5,1141439
edited Jan 6 at 23:08
clathratus
5,1141439
5,1141439
asked May 13 '14 at 13:01
KinKin
55431431
asked May 13 '14 at 13:01
KinKin
55431431
asked May 13 '14 at 13:01
KinKin
55431431
55431431
$begingroup$
sosmath.com/CBB/viewtopic.php?p=47786
$endgroup$
– lab bhattacharjee
May 13 '14 at 13:03
add a comment |
$begingroup$
sosmath.com/CBB/viewtopic.php?p=47786
$endgroup$
– lab bhattacharjee
May 13 '14 at 13:03
$begingroup$
sosmath.com/CBB/viewtopic.php?p=47786
$endgroup$
– lab bhattacharjee
May 13 '14 at 13:03
$begingroup$
sosmath.com/CBB/viewtopic.php?p=47786
$endgroup$
– lab bhattacharjee
May 13 '14 at 13:03
add a comment |
1 Answer
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HINT: Since $$frac{d}{dtheta}tan theta=sec^2theta$$, you have $$int sec^2theta tan^{n-2}theta dtheta=int tan^{n-2}theta d(tantheta)$$
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
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1 Answer
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1 Answer
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active
oldest
votes
active
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active
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votes
$begingroup$
HINT: Since $$frac{d}{dtheta}tan theta=sec^2theta$$, you have $$int sec^2theta tan^{n-2}theta dtheta=int tan^{n-2}theta d(tantheta)$$
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
$endgroup$
add a comment |
$begingroup$
HINT: Since $$frac{d}{dtheta}tan theta=sec^2theta$$, you have $$int sec^2theta tan^{n-2}theta dtheta=int tan^{n-2}theta d(tantheta)$$
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
$endgroup$
add a comment |
$begingroup$
HINT: Since $$frac{d}{dtheta}tan theta=sec^2theta$$, you have $$int sec^2theta tan^{n-2}theta dtheta=int tan^{n-2}theta d(tantheta)$$
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
$endgroup$
HINT: Since $$frac{d}{dtheta}tan theta=sec^2theta$$, you have $$int sec^2theta tan^{n-2}theta dtheta=int tan^{n-2}theta d(tantheta)$$
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
answered May 13 '14 at 13:04
Samrat MukhopadhyaySamrat Mukhopadhyay
13.8k2047
13.8k2047
add a comment |
add a comment |
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– lab bhattacharjee
May 13 '14 at 13:03