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If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equation
- a)x2 – 6x + 1 = 0
- b)6x2 – x – 1 = 0
- c)6x2 + x + 1 = 0
- d)x2 – x + 6 = 0
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of ...
Given Information:
The given equation is sin θ + 7 cos θ = 5.
To find:
We need to determine which of the given options has the root as tan (θ/2).
Solution:
Step 1: Convert sin θ + 7 cos θ = 5 into a more suitable form.
We know that sin θ = 2tan (θ/2) / (1 + tan^2(θ/2)) and cos θ = (1 - tan^2(θ/2)) / (1 + tan^2(θ/2)).
Substitute these values in the given equation sin θ + 7 cos θ = 5:
2tan (θ/2) / (1 + tan^2(θ/2)) + 7[(1 - tan^2(θ/2)) / (1 + tan^2(θ/2))] = 5.
Step 2: Simplify the equation.
2tan (θ/2) + 7(1 - tan^2(θ/2)) = 5(1 + tan^2(θ/2)).
2tan (θ/2) + 7 - 7tan^2(θ/2) = 5 + 5tan^2(θ/2).
Rearrange the terms:
12tan^2(θ/2) - 6tan(θ/2) - 2 = 0.
Step 3: Compare with given options.
The above equation matches with option B: 6x^2 - x - 1 = 0.
Conclusion:
Therefore, the correct answer is option B: 6x^2 - x - 1 = 0, as tan (θ/2) is a root of this equation.
The given equation is sin θ + 7 cos θ = 5.
To find:
We need to determine which of the given options has the root as tan (θ/2).
Solution:
Step 1: Convert sin θ + 7 cos θ = 5 into a more suitable form.
We know that sin θ = 2tan (θ/2) / (1 + tan^2(θ/2)) and cos θ = (1 - tan^2(θ/2)) / (1 + tan^2(θ/2)).
Substitute these values in the given equation sin θ + 7 cos θ = 5:
2tan (θ/2) / (1 + tan^2(θ/2)) + 7[(1 - tan^2(θ/2)) / (1 + tan^2(θ/2))] = 5.
Step 2: Simplify the equation.
2tan (θ/2) + 7(1 - tan^2(θ/2)) = 5(1 + tan^2(θ/2)).
2tan (θ/2) + 7 - 7tan^2(θ/2) = 5 + 5tan^2(θ/2).
Rearrange the terms:
12tan^2(θ/2) - 6tan(θ/2) - 2 = 0.
Step 3: Compare with given options.
The above equation matches with option B: 6x^2 - x - 1 = 0.
Conclusion:
Therefore, the correct answer is option B: 6x^2 - x - 1 = 0, as tan (θ/2) is a root of this equation.
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If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer?
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If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer?.
If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer?.
Solutions for If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equationa)x2–6x + 1 = 0b)6x2–x –1 = 0c)6x2+ x + 1 = 0d)x2–x + 6 = 0Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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