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If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2?
Most Upvoted Answer
If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 ...
Solution:
Given, angle B = 45° in triangle ABC.
We know that the sum of all angles in a triangle is 180°.
Therefore, angle A + angle B + angle C = 180°.
Substituting angle B = 45°, we get:
angle A + 45° + angle C = 180°
angle A + angle C = 135°
Now, we need to find the value of (1/cot A) (1/cot C).
Let us first simplify this expression.
(1/cot A) (1/cot C) = (1/tan A) (1/tan C) [Since cot A = 1/tan A and cot C = 1/tan C]
= 1/(tan A tan C)
We know that tan (A + C) = (tan A + tan C)/(1 - tan A tan C)
Substituting angle A + angle C = 135°, we get:
tan 135° = (tan A + tan C)/(1 - tan A tan C)
Since tan 135° = -1, we can write:
-1 = (tan A + tan C)/(1 - tan A tan C)
Simplifying this equation, we get:
tan A tan C + tan A + tan C + 1 = 0
Now, let us try to find the value of (1/cot A) (1/cot C) using the given equation.
(1/cot A) (1/cot C) = (1/tan A) (1/tan C)
= 1/(tan A tan C)
= -1/(tan A + tan C + 1)
We know that tan A + tan C + 1 = -tan A tan C.
Therefore, (1/cot A) (1/cot C) = -1/(-tan A tan C) = 1
Hence, the value of (1/cot A) (1/cot C) is 1.
Therefore, the correct option is 2) 1.
Note: HTML tags cannot be used in plain text response.
Given, angle B = 45° in triangle ABC.
We know that the sum of all angles in a triangle is 180°.
Therefore, angle A + angle B + angle C = 180°.
Substituting angle B = 45°, we get:
angle A + 45° + angle C = 180°
angle A + angle C = 135°
Now, we need to find the value of (1/cot A) (1/cot C).
Let us first simplify this expression.
(1/cot A) (1/cot C) = (1/tan A) (1/tan C) [Since cot A = 1/tan A and cot C = 1/tan C]
= 1/(tan A tan C)
We know that tan (A + C) = (tan A + tan C)/(1 - tan A tan C)
Substituting angle A + angle C = 135°, we get:
tan 135° = (tan A + tan C)/(1 - tan A tan C)
Since tan 135° = -1, we can write:
-1 = (tan A + tan C)/(1 - tan A tan C)
Simplifying this equation, we get:
tan A tan C + tan A + tan C + 1 = 0
Now, let us try to find the value of (1/cot A) (1/cot C) using the given equation.
(1/cot A) (1/cot C) = (1/tan A) (1/tan C)
= 1/(tan A tan C)
= -1/(tan A + tan C + 1)
We know that tan A + tan C + 1 = -tan A tan C.
Therefore, (1/cot A) (1/cot C) = -1/(-tan A tan C) = 1
Hence, the value of (1/cot A) (1/cot C) is 1.
Therefore, the correct option is 2) 1.
Note: HTML tags cannot be used in plain text response.
Community Answer
If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 ...
Option b
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If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2?
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If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2?.
If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If m angle B=45 of triangle ABC,then(1 cotA)(1 cotC)=? 1)0 2)1 3)-1 4)2?.
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