JEE Exam > JEE Questions > If [sin-1 cos-1 sin-1 tan-1x]= 1, ë&ucir...
Start Learning for Free
If [sin-1 cos-1 sin-1 tan-1x] = 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.
- a)[tan sin cos1, tan sin cos sin1]
- b)[tan sin cos1, tan sin cos sin 2]
- c)[-1,1]
- d)[sin cos tan1, sin cos sin tan1]
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the ...
[x] = K, K ∈ Z ⇒ K < x < K + 1, where [x] represents integer part of x.
Most Upvoted Answer
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the ...
[x] = K, K ∈ Z ⇒ K < x="" />< k="" +="" 1,="" where="" [x]="" represents="" integer="" part="" of="" x.="" k="" +="" 1,="" where="" [x]="" represents="" integer="" part="" of="" />
Free Test
FREE
| Start Free Test |
Community Answer
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the ...
Understanding the Given Equation
The equation to solve is [sin-1 cos-1 sin-1 tan-1x] = 1, where the brackets denote the greatest integer function. The aim is to determine the interval for x.
Step 1: Analyze the Components
- sin-1: The inverse sine function has a range of [-π/2, π/2].
- cos-1: The inverse cosine function ranges from [0, π].
- tan-1x: The inverse tangent function ranges from (-π/2, π/2).
Step 2: Evaluating the Expression
The expression sin-1(cos-1(sin-1(tan-1x))) needs to be simplified:
1. tan-1(x) gives an angle θ such that tan(θ) = x.
2. sin-1(tan-1(x)) will yield values between -π/2 and π/2.
Next, consider cos-1(sin-1(...)). The output of sin-1 is in [0, π/2], which is suitable for the cos-1 function.
Finally, the outer sin-1 function will limit the range to [-π/2, π/2].
Step 3: Applying the Greatest Integer Function
Given that the entire expression evaluates to 1, the output must be in the range of [1, 2) for the greatest integer function to yield 1.
Step 4: Finding the Interval for x
To satisfy the condition:
- The inner expressions must yield values that fall within the required range.
- By analyzing the ranges of transformations through sin and cos functions, we see that the values of x must be confined within reasonable trigonometric limits.
Conclusion
Based on the analysis, the correct interval for x is:
- Option A: [tan(sin(cos(1))), tan(sin(cos(sin(1))))]
This interval ensures that the output of the nested functions meets the criteria for the greatest integer function to equal 1.
The equation to solve is [sin-1 cos-1 sin-1 tan-1x] = 1, where the brackets denote the greatest integer function. The aim is to determine the interval for x.
Step 1: Analyze the Components
- sin-1: The inverse sine function has a range of [-π/2, π/2].
- cos-1: The inverse cosine function ranges from [0, π].
- tan-1x: The inverse tangent function ranges from (-π/2, π/2).
Step 2: Evaluating the Expression
The expression sin-1(cos-1(sin-1(tan-1x))) needs to be simplified:
1. tan-1(x) gives an angle θ such that tan(θ) = x.
2. sin-1(tan-1(x)) will yield values between -π/2 and π/2.
Next, consider cos-1(sin-1(...)). The output of sin-1 is in [0, π/2], which is suitable for the cos-1 function.
Finally, the outer sin-1 function will limit the range to [-π/2, π/2].
Step 3: Applying the Greatest Integer Function
Given that the entire expression evaluates to 1, the output must be in the range of [1, 2) for the greatest integer function to yield 1.
Step 4: Finding the Interval for x
To satisfy the condition:
- The inner expressions must yield values that fall within the required range.
- By analyzing the ranges of transformations through sin and cos functions, we see that the values of x must be confined within reasonable trigonometric limits.
Conclusion
Based on the analysis, the correct interval for x is:
- Option A: [tan(sin(cos(1))), tan(sin(cos(sin(1))))]
This interval ensures that the output of the nested functions meets the criteria for the greatest integer function to equal 1.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer?
Question Description
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. 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 If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer?.
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. 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 If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer?.
Solutions for If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If [sin-1 cos-1 sin-1 tan-1x]= 1, ëû where [.] denotes the greatest integer function, then x belongs to the interval.a)[tan sin cos1, tan sin cos sin1]b)[tan sin cos1, tan sin cos sin 2]c)[-1,1]d)[sin cos tan1, sin cos sin tan1]Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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