Class 10 Exam > Class 10 Questions > Directions: In the following questions, A st...
Start Learning for Free
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The value of tan47γ/cot43γ is 1.
Reason (R): The value of the expression (sin 80° – cos 80°) is negative.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Directions: In the following questions, A statement of Assertion (A) ...
In case of assertion
View all questions of this test
∴ Assertion is correct.
In case of reason:
80° is near to 90°, sin 90° = 1 and cos 90° = 0
So, the given expression sin 80° – cos 80° > 0
So, the value of the given expression is positive.
∴ Reason is incorrect:
Hence, the assertion is correct but the reason is incorrect.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion and Reasoning:
Assertion (A): The value of tan47γ/cot43γ is 1.
Reasoning (R): The value of the expression (sin 80° – cos 80°) is negative.
Explanation:
Let's simplify the expression tan47γ/cot43γ.
tan47γ = sin47γ/cos47γ
cot43γ = cos43γ/sin43γ
tan47γ/cot43γ = (sin47γ/cos47γ)/(cos43γ/sin43γ)
tan47γ/cot43γ = sin47γ/sin43γ * cos43γ/cos47γ
tan47γ/cot43γ = tan(47γ - 43γ)
tan47γ/cot43γ = tan4γ
Now, we need to find the value of tan4γ to check if it is equal to 1 or not.
tan4γ = tan(45° + 1°)
tan4γ = (tan45° + tan1°)/(1 - tan45° * tan1°)
tan4γ = (1 + tan1°)/(1 - 1 * tan1°)
tan4γ = (1 + tan1°)/(1 - tan1°)
We cannot simplify this expression any further, but we can use a calculator to find its value, which is approximately equal to 1.003.
Therefore, the assertion (A) is true.
Now, let's check the reasoning (R) which says that the value of the expression (sin 80° – cos 80°) is negative.
sin 80° = 0.9848
cos 80° = 0.1736
sin 80° – cos 80° = 0.9848 – 0.1736
sin 80° – cos 80° = 0.8112
The value of (sin 80° – cos 80°) is positive, not negative. Therefore, the reasoning (R) is false.
Conclusion:
Both assertion (A) and reasoning (R) are true, but the reasoning (R) is not the correct explanation of the assertion (A). Hence, option (C) is the correct answer.
Assertion (A): The value of tan47γ/cot43γ is 1.
Reasoning (R): The value of the expression (sin 80° – cos 80°) is negative.
Explanation:
Let's simplify the expression tan47γ/cot43γ.
tan47γ = sin47γ/cos47γ
cot43γ = cos43γ/sin43γ
tan47γ/cot43γ = (sin47γ/cos47γ)/(cos43γ/sin43γ)
tan47γ/cot43γ = sin47γ/sin43γ * cos43γ/cos47γ
tan47γ/cot43γ = tan(47γ - 43γ)
tan47γ/cot43γ = tan4γ
Now, we need to find the value of tan4γ to check if it is equal to 1 or not.
tan4γ = tan(45° + 1°)
tan4γ = (tan45° + tan1°)/(1 - tan45° * tan1°)
tan4γ = (1 + tan1°)/(1 - 1 * tan1°)
tan4γ = (1 + tan1°)/(1 - tan1°)
We cannot simplify this expression any further, but we can use a calculator to find its value, which is approximately equal to 1.003.
Therefore, the assertion (A) is true.
Now, let's check the reasoning (R) which says that the value of the expression (sin 80° – cos 80°) is negative.
sin 80° = 0.9848
cos 80° = 0.1736
sin 80° – cos 80° = 0.9848 – 0.1736
sin 80° – cos 80° = 0.8112
The value of (sin 80° – cos 80°) is positive, not negative. Therefore, the reasoning (R) is false.
Conclusion:
Both assertion (A) and reasoning (R) are true, but the reasoning (R) is not the correct explanation of the assertion (A). Hence, option (C) is the correct answer.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?
Question Description
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The value of tan47γ/cot43γ is 1.Reason (R): The value of the expression (sin 80° – cos 80°) is negative.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup