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In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C?
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In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + ...
Given Information:
In an acute angled triangle ABC,
- sin (2A + B - C) = 1
- tan (B + C - A) = √3
Solution:
Using Trigonometric Identities:
We know that sin2x + cos2x = 1
Therefore, sin2A + cos2A = 1
=> 1 - cos2A + cos2A = 1
=> cos2A = 0
=> cosA = 0
=> A = 90°
Using tan(B + C - A) = √3:
tan(B + C - 90°) = √3
tan(B + C - 90°) = tan60°
B + C - 90° = 60°
B + C = 150°
Using sin(2A + B - C) = 1:
sin(2*90° + 150° - C) = 1
sin(180° + 150° - C) = 1
sin(330° - C) = 1
sin(30°) = 1
C = 30°
Final Values:
A = 90°
B = 60°
C = 30°
Therefore, the values of A, B, and C in the acute-angled triangle ABC are 90°, 60°, and 30° respectively.
In an acute angled triangle ABC,
- sin (2A + B - C) = 1
- tan (B + C - A) = √3
Solution:
Using Trigonometric Identities:
We know that sin2x + cos2x = 1
Therefore, sin2A + cos2A = 1
=> 1 - cos2A + cos2A = 1
=> cos2A = 0
=> cosA = 0
=> A = 90°
Using tan(B + C - A) = √3:
tan(B + C - 90°) = √3
tan(B + C - 90°) = tan60°
B + C - 90° = 60°
B + C = 150°
Using sin(2A + B - C) = 1:
sin(2*90° + 150° - C) = 1
sin(180° + 150° - C) = 1
sin(330° - C) = 1
sin(30°) = 1
C = 30°
Final Values:
A = 90°
B = 60°
C = 30°
Therefore, the values of A, B, and C in the acute-angled triangle ABC are 90°, 60°, and 30° respectively.
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In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C?
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In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C?.
In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an acute angled triangle ABC, if sin (2A + B - C) = 1 and tan (B + C - A) = √3. then find the values of A, B and C?.
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