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Triangle ABC, right angled at C, then the value of cosec (A + B) is?
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Triangle ABC, right angled at C, then the value of cosec (A + B) is?
Given Information:
- Triangle ABC is right-angled at C.
To find:
The value of cosec(A + B).
Explanation:
Step 1: Finding the values of angles A, B, and C:
- In a right-angled triangle, angle C is 90 degrees.
- Since the sum of angles in a triangle is 180 degrees, we can find the values of angles A and B.
- Therefore, A + B + 90 = 180
- A + B = 90
Step 2: Finding the value of cosec(A + B):
- We know that cosec(x) = 1/sin(x).
- Therefore, cosec(A + B) = 1/sin(A + B).
Step 3: Finding the value of sin(A + B):
- Using the trigonometric identity sin(A + B) = sinAcosB + cosAsinB.
- In this case, since A + B = 90 degrees, sin(A + B) = sin90 = 1.
Step 4: Finding the value of cosec(A + B):
- Therefore, cosec(A + B) = 1/sin(A + B) = 1/1 = 1.
Conclusion:
- The value of cosec(A + B) in a right-angled triangle ABC is 1.
- Triangle ABC is right-angled at C.
To find:
The value of cosec(A + B).
Explanation:
Step 1: Finding the values of angles A, B, and C:
- In a right-angled triangle, angle C is 90 degrees.
- Since the sum of angles in a triangle is 180 degrees, we can find the values of angles A and B.
- Therefore, A + B + 90 = 180
- A + B = 90
Step 2: Finding the value of cosec(A + B):
- We know that cosec(x) = 1/sin(x).
- Therefore, cosec(A + B) = 1/sin(A + B).
Step 3: Finding the value of sin(A + B):
- Using the trigonometric identity sin(A + B) = sinAcosB + cosAsinB.
- In this case, since A + B = 90 degrees, sin(A + B) = sin90 = 1.
Step 4: Finding the value of cosec(A + B):
- Therefore, cosec(A + B) = 1/sin(A + B) = 1/1 = 1.
Conclusion:
- The value of cosec(A + B) in a right-angled triangle ABC is 1.
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Triangle ABC, right angled at C, then the value of cosec (A + B) is?
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Triangle ABC, right angled at C, then the value of cosec (A + B) is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC, right angled at C, then the value of cosec (A + B) is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC, right angled at C, then the value of cosec (A + B) is?.
Triangle ABC, right angled at C, then the value of cosec (A + B) is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC, right angled at C, then the value of cosec (A + B) is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC, right angled at C, then the value of cosec (A + B) is?.
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