Is there a way of reducing $4sin(a)sin(b)-sin(a+c)sin(b)-sin(a)sin(b+d)$ using the gonionmetric identities?
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I'm currently working on a problem and stumbled on this equation that I'm unable to reduce using the standard goniometric identities. Perhaps the formula is impossible to reduce but any help is appreciated.
The formula I'm trying to reduce:
$$Av^{h}_{i}=4sin(a)sin(b)-sin(a+c)sin(b)-sin(a)sin(b+d)$$
[added from a comment: I've got $a=pi ki$, $b=pi kl$, $c=pi k$, and $d=pi l$, where $i$, $j$, $k$, $l$ are positive integers.]
I've tried to use the identity:
$$sin(a+b)+sin(a-b)=2sin(a)cos(b)$$
But this doesn't get me any further than a massive mess of equations. Again, perhaps the equation cannot be reduced further, but my teacher pointed out that it is indeed possible, it just takes alot of writing.
Any help is appreciated.
trigonometry
edited Nov 16 at 11:21
Blue
47k870148
asked Nov 15 at 13:25
S. Crim
10110
add a comment |
up vote
1
down vote
favorite
I'm currently working on a problem and stumbled on this equation that I'm unable to reduce using the standard goniometric identities. Perhaps the formula is impossible to reduce but any help is appreciated.
The formula I'm trying to reduce:
$$Av^{h}_{i}=4sin(a)sin(b)-sin(a+c)sin(b)-sin(a)sin(b+d)$$
[added from a comment: I've got $a=pi ki$, $b=pi kl$, $c=pi k$, and $d=pi l$, where $i$, $j$, $k$, $l$ are positive integers.]
I've tried to use the identity:
$$sin(a+b)+sin(a-b)=2sin(a)cos(b)$$
But this doesn't get me any further than a massive mess of equations. Again, perhaps the equation cannot be reduced further, but my teacher pointed out that it is indeed possible, it just takes alot of writing.
Any help is appreciated.
trigonometry
edited Nov 16 at 11:21
Blue
47k870148
asked Nov 15 at 13:25
S. Crim
10110
Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
2
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm currently working on a problem and stumbled on this equation that I'm unable to reduce using the standard goniometric identities. Perhaps the formula is impossible to reduce but any help is appreciated.
The formula I'm trying to reduce:
$$Av^{h}_{i}=4sin(a)sin(b)-sin(a+c)sin(b)-sin(a)sin(b+d)$$
[added from a comment: I've got $a=pi ki$, $b=pi kl$, $c=pi k$, and $d=pi l$, where $i$, $j$, $k$, $l$ are positive integers.]
I've tried to use the identity:
$$sin(a+b)+sin(a-b)=2sin(a)cos(b)$$
But this doesn't get me any further than a massive mess of equations. Again, perhaps the equation cannot be reduced further, but my teacher pointed out that it is indeed possible, it just takes alot of writing.
Any help is appreciated.
trigonometry
edited Nov 16 at 11:21
Blue
47k870148
asked Nov 15 at 13:25
S. Crim
10110
I'm currently working on a problem and stumbled on this equation that I'm unable to reduce using the standard goniometric identities. Perhaps the formula is impossible to reduce but any help is appreciated.
The formula I'm trying to reduce:
$$Av^{h}_{i}=4sin(a)sin(b)-sin(a+c)sin(b)-sin(a)sin(b+d)$$
[added from a comment: I've got $a=pi ki$, $b=pi kl$, $c=pi k$, and $d=pi l$, where $i$, $j$, $k$, $l$ are positive integers.]
I've tried to use the identity:
$$sin(a+b)+sin(a-b)=2sin(a)cos(b)$$
But this doesn't get me any further than a massive mess of equations. Again, perhaps the equation cannot be reduced further, but my teacher pointed out that it is indeed possible, it just takes alot of writing.
Any help is appreciated.
trigonometry
trigonometry
edited Nov 16 at 11:21
Blue
47k870148
asked Nov 15 at 13:25
S. Crim
10110
edited Nov 16 at 11:21
Blue
47k870148
asked Nov 15 at 13:25
S. Crim
10110
edited Nov 16 at 11:21
Blue
47k870148
edited Nov 16 at 11:21
Blue
47k870148
edited Nov 16 at 11:21
Blue
47k870148
47k870148
asked Nov 15 at 13:25
S. Crim
10110
asked Nov 15 at 13:25
S. Crim
10110
asked Nov 15 at 13:25
S. Crim
10110
10110
Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
2
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45
add a comment |
Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
2
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45
Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
2
2
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45
add a comment |
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Wolfram Alpha also come up with nothing really useful. Do you have any additional information, such as relationships among $a, b, c, d$? For example (as a wild guess), are they the four angles of a quadrilateral?
– David K
Nov 15 at 15:20
@DavidK I might have something for them but probably nothing useful either. I've got: $a=pi k i$, $b=pi k l$, $c=pi k$ and $d=pi l$, where $i,j,k,l$ are positive integers.
– S. Crim
Nov 15 at 19:23
2
$sin(npi) = 0$ for any integer $n.$ That would simplify your formula rather dramatically!
– David K
Nov 15 at 21:45