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In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3 x - k = 0, 0 < k < 1, then value of C is
- a)π/3
- b)π/2
- c)2π/3
- d)5π/6
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Triangle Angles
In triangle ABC, the relationship between the angles is defined by the condition that angle B is greater than angle A. Therefore, we can express this as:
- Angle A < angle="" b="" />< angle="" />
- Angle C = 180° - (Angle A + Angle B)
Equation Analysis
The angles A and B satisfy the equation:
- 3 sin x - 4 sin(3x) - k = 0, with 0 < k="" />< />
This equation can be restructured using trigonometric identities. The term sin(3x) can be expressed as:
- sin(3x) = 3 sin x - 4 sin^3 x.
Substituting this into the equation yields:
- 3 sin x - 4(3 sin x - 4 sin^3 x) - k = 0.
This simplifies to:
- -9 sin x + 16 sin^3 x - k = 0.
Finding Angles A and B
To solve for the angles A and B, consider the nature of the sine function and its values constrained by k. The maximum value of sin x is 1. As k is less than 1, it indicates that angles A and B must be such that they yield a sum of sines that meets this equation.
Given the constraints and the relationship between angles:
- The angle C can be calculated as 180° - (A + B), ensuring that C remains the largest angle.
Determining Angle C
From the sine equation, we can deduce that if angles A and B are complementary such that they sum up to 60°, angle C must be:
- C = 180° - (A + B) = 180° - 120° = 60°.
Thus, in radians, angle C equals:
- C = π/3.
Hence, the correct answer is:
Correct Answer: Option C: 2π/3.
In triangle ABC, the relationship between the angles is defined by the condition that angle B is greater than angle A. Therefore, we can express this as:
- Angle A < angle="" b="" />< angle="" />
- Angle C = 180° - (Angle A + Angle B)
Equation Analysis
The angles A and B satisfy the equation:
- 3 sin x - 4 sin(3x) - k = 0, with 0 < k="" />< />
This equation can be restructured using trigonometric identities. The term sin(3x) can be expressed as:
- sin(3x) = 3 sin x - 4 sin^3 x.
Substituting this into the equation yields:
- 3 sin x - 4(3 sin x - 4 sin^3 x) - k = 0.
This simplifies to:
- -9 sin x + 16 sin^3 x - k = 0.
Finding Angles A and B
To solve for the angles A and B, consider the nature of the sine function and its values constrained by k. The maximum value of sin x is 1. As k is less than 1, it indicates that angles A and B must be such that they yield a sum of sines that meets this equation.
Given the constraints and the relationship between angles:
- The angle C can be calculated as 180° - (A + B), ensuring that C remains the largest angle.
Determining Angle C
From the sine equation, we can deduce that if angles A and B are complementary such that they sum up to 60°, angle C must be:
- C = 180° - (A + B) = 180° - 120° = 60°.
Thus, in radians, angle C equals:
- C = π/3.
Hence, the correct answer is:
Correct Answer: Option C: 2π/3.
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In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer?
Question Description
In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer?.
In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer?.
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In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x - 4 sin3x - k = 0, 0 < k < 1, then value of C isa)π/3b)π/2c)2π/3d)5π/6Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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