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If $A+B+C=180^circ$, then $fractan A + tan B + tan Ctan A tan B tan C equiv 1$ [closed]
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If the sum of $A$, $B$, and $C$ is $180^circ$, then prove that $$fractan A + tan B + tan Ctan A tan B tan C = 1.$$
trigonometry
edited Jul 27 at 17:22
Math Lover
12.3k21232
asked Jul 27 at 16:41
CubbyKushi
1
closed as off-topic by B. Goddard, The Phenotype, Xander Henderson, José Carlos Santos, Mostafa Ayaz Jul 27 at 17:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." РB. Goddard, The Phenotype, Xander Henderson, Jos̩ Carlos Santos, Mostafa Ayaz
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up vote
-2
down vote
favorite
If the sum of $A$, $B$, and $C$ is $180^circ$, then prove that $$fractan A + tan B + tan Ctan A tan B tan C = 1.$$
trigonometry
edited Jul 27 at 17:22
Math Lover
12.3k21232
asked Jul 27 at 16:41
CubbyKushi
1
closed as off-topic by B. Goddard, The Phenotype, Xander Henderson, José Carlos Santos, Mostafa Ayaz Jul 27 at 17:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." РB. Goddard, The Phenotype, Xander Henderson, Jos̩ Carlos Santos, Mostafa Ayaz
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
1
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34
 |Â
show 1 more comment
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
If the sum of $A$, $B$, and $C$ is $180^circ$, then prove that $$fractan A + tan B + tan Ctan A tan B tan C = 1.$$
trigonometry
edited Jul 27 at 17:22
Math Lover
12.3k21232
asked Jul 27 at 16:41
CubbyKushi
1
If the sum of $A$, $B$, and $C$ is $180^circ$, then prove that $$fractan A + tan B + tan Ctan A tan B tan C = 1.$$
trigonometry
edited Jul 27 at 17:22
Math Lover
12.3k21232
asked Jul 27 at 16:41
CubbyKushi
1
edited Jul 27 at 17:22
Math Lover
12.3k21232
edited Jul 27 at 17:22
Math Lover
12.3k21232
edited Jul 27 at 17:22
Math Lover
12.3k21232
12.3k21232
asked Jul 27 at 16:41
CubbyKushi
1
asked Jul 27 at 16:41
CubbyKushi
1
asked Jul 27 at 16:41
CubbyKushi
1
1
closed as off-topic by B. Goddard, The Phenotype, Xander Henderson, José Carlos Santos, Mostafa Ayaz Jul 27 at 17:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." РB. Goddard, The Phenotype, Xander Henderson, Jos̩ Carlos Santos, Mostafa Ayaz
closed as off-topic by B. Goddard, The Phenotype, Xander Henderson, José Carlos Santos, Mostafa Ayaz Jul 27 at 17:04
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." РB. Goddard, The Phenotype, Xander Henderson, Jos̩ Carlos Santos, Mostafa Ayaz
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
1
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34
 |Â
show 1 more comment
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
1
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
1
1
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34
 |Â
show 1 more comment
2 Answers
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$$A+B+C=180^circ$$
$$tan A+B+C=tan180^circ$$
$$fractan A+tan B+tan C-tan Atan Btan C1-tan A+tan B-tan Btan C-tan Atan C=0$$
$$tan A+tan B+tan C=tan Atan Btan C$$
$$dfractan A+tan B+tan Ctan Atan Btan C=1$$
answered Jul 27 at 16:56
Key Flex
4,015423
add a comment |Â
up vote
0
down vote
Write $A+B = 180 - C$ . Take tan on both sides . Expand the LHS and you shall get your identity proved.
By the way $tan(A+B)= (tan A+ tan B)/(1-tan Atan B)$
edited Jul 27 at 17:02
Key Flex
4,015423
answered Jul 27 at 16:56
Akash Roy
156
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
$$A+B+C=180^circ$$
$$tan A+B+C=tan180^circ$$
$$fractan A+tan B+tan C-tan Atan Btan C1-tan A+tan B-tan Btan C-tan Atan C=0$$
$$tan A+tan B+tan C=tan Atan Btan C$$
$$dfractan A+tan B+tan Ctan Atan Btan C=1$$
answered Jul 27 at 16:56
Key Flex
4,015423
add a comment |Â
up vote
1
down vote
$$A+B+C=180^circ$$
$$tan A+B+C=tan180^circ$$
$$fractan A+tan B+tan C-tan Atan Btan C1-tan A+tan B-tan Btan C-tan Atan C=0$$
$$tan A+tan B+tan C=tan Atan Btan C$$
$$dfractan A+tan B+tan Ctan Atan Btan C=1$$
answered Jul 27 at 16:56
Key Flex
4,015423
add a comment |Â
up vote
1
down vote
up vote
1
down vote
$$A+B+C=180^circ$$
$$tan A+B+C=tan180^circ$$
$$fractan A+tan B+tan C-tan Atan Btan C1-tan A+tan B-tan Btan C-tan Atan C=0$$
$$tan A+tan B+tan C=tan Atan Btan C$$
$$dfractan A+tan B+tan Ctan Atan Btan C=1$$
answered Jul 27 at 16:56
Key Flex
4,015423
$$A+B+C=180^circ$$
$$tan A+B+C=tan180^circ$$
$$fractan A+tan B+tan C-tan Atan Btan C1-tan A+tan B-tan Btan C-tan Atan C=0$$
$$tan A+tan B+tan C=tan Atan Btan C$$
$$dfractan A+tan B+tan Ctan Atan Btan C=1$$
answered Jul 27 at 16:56
Key Flex
4,015423
answered Jul 27 at 16:56
Key Flex
4,015423
answered Jul 27 at 16:56
Key Flex
4,015423
answered Jul 27 at 16:56
Key Flex
4,015423
4,015423
add a comment |Â
add a comment |Â
up vote
0
down vote
Write $A+B = 180 - C$ . Take tan on both sides . Expand the LHS and you shall get your identity proved.
By the way $tan(A+B)= (tan A+ tan B)/(1-tan Atan B)$
edited Jul 27 at 17:02
Key Flex
4,015423
answered Jul 27 at 16:56
Akash Roy
156
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
add a comment |Â
up vote
0
down vote
Write $A+B = 180 - C$ . Take tan on both sides . Expand the LHS and you shall get your identity proved.
By the way $tan(A+B)= (tan A+ tan B)/(1-tan Atan B)$
edited Jul 27 at 17:02
Key Flex
4,015423
answered Jul 27 at 16:56
Akash Roy
156
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Write $A+B = 180 - C$ . Take tan on both sides . Expand the LHS and you shall get your identity proved.
By the way $tan(A+B)= (tan A+ tan B)/(1-tan Atan B)$
edited Jul 27 at 17:02
Key Flex
4,015423
answered Jul 27 at 16:56
Akash Roy
156
Write $A+B = 180 - C$ . Take tan on both sides . Expand the LHS and you shall get your identity proved.
By the way $tan(A+B)= (tan A+ tan B)/(1-tan Atan B)$
edited Jul 27 at 17:02
Key Flex
4,015423
answered Jul 27 at 16:56
Akash Roy
156
edited Jul 27 at 17:02
Key Flex
4,015423
edited Jul 27 at 17:02
Key Flex
4,015423
edited Jul 27 at 17:02
Key Flex
4,015423
4,015423
answered Jul 27 at 16:56
Akash Roy
156
answered Jul 27 at 16:56
Akash Roy
156
answered Jul 27 at 16:56
Akash Roy
156
156
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
add a comment |Â
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
It might be difficult to expand tan(A+B+C) as it might have lot of terms to handle.
– Akash Roy
Jul 27 at 16:57
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
tan(180-C)=-tan C for your information.
– Akash Roy
Jul 27 at 16:58
add a comment |Â
Welcome to MSE! Please visit the Help Center page on how to ask a good question.
– Robert Howard
Jul 27 at 16:46
Hey, why and how should anyone help you if you don't show your own approach to the problem.
– Harshit Joshi
Jul 27 at 16:48
Find $tan (A+B+C)$
– Doug M
Jul 27 at 16:48
1
Also, this is a duplicate.
– Blue
Jul 27 at 17:20
@Harshit Joshi I have no approach or rather I had no approach. I was completely stuck.
– CubbyKushi
Jul 27 at 17:34