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If [sin−1cos−1sin−1tan−1x] = 1, where [.]. denotes the greatest integer function, then the set of all the values of x is
  • a)
    [tan{sin(cos1)}, tan[sin{cos(sin1)}]]
  • b)
    (tan{sin(cos1)}, tan[sin{cos(sin1)}])
  • c)
    [−1, 1]
  • d)
    [sin{cos(tan1)}, sin[cos{sin(tan1)}]]
Correct answer is option 'A'. Can you explain this answer?
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If[sin−1cos−1sin−1tan−1x] = 1, where[.].denote...
Given, that
[sin−1cos−1sin−1tan−1x] = 1

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If[sin−1cos−1sin−1tan−1x] = 1, where[.].denote...
Explanation:

Finding the Domain:
- The given expression involves multiple inverse trigonometric functions within the greatest integer function.
- To find the domain of x, we need to analyze the ranges of each trigonometric function involved.

Analysis of Trigonometric Functions:
- The range of sin^-1 function is [-π/2, π/2].
- The range of cos^-1 function is [0, π].
- The range of tan^-1 function is (-π/2, π/2).

Combining Trigonometric Functions:
- sin^-1(cos^-1(sin^-1(x))) = 1
- sin^-1(cos^-1(sin^-1(x))) = sin^-1(cos^-1(1)) = sin^-1(0) = 0

Expression Simplification:
- sin^-1(cos^-1(sin^-1(x))) = 1 simplifies to sin^-1(0) = 1

Identifying the Set of Values:
- The set of values of x will be the range of the expression sin^-1(cos^-1(sin^-1(x))) = 1.
- This simplifies to sin^-1(0) = 1, which implies x = sin(0) = 0.

Final Range of Values:
- The set of all values of x is within the interval [0, 0].
- Therefore, the correct option is (tan{sin(cos1)}, tan[sin{cos(sin1)}]).
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If[sin−1cos−1sin−1tan−1x] = 1, where[.].denotes the greatest integer function, then theset of all the values ofx isa)[tan{sin(cos1)}, tan[sin{cos(sin1)}]]b)(tan{sin(cos1)}, tan[sin{cos(sin1)}])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−1cos−1sin−1tan−1x] = 1, where[.].denotes the greatest integer function, then theset of all the values ofx isa)[tan{sin(cos1)}, tan[sin{cos(sin1)}]]b)(tan{sin(cos1)}, tan[sin{cos(sin1)}])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−1cos−1sin−1tan−1x] = 1, where[.].denotes the greatest integer function, then theset of all the values ofx isa)[tan{sin(cos1)}, tan[sin{cos(sin1)}]]b)(tan{sin(cos1)}, tan[sin{cos(sin1)}])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−1cos−1sin−1tan−1x] = 1, where[.].denotes the greatest integer function, then theset of all the values ofx isa)[tan{sin(cos1)}, tan[sin{cos(sin1)}]]b)(tan{sin(cos1)}, tan[sin{cos(sin1)}])c)[−1, 1]d)[sin{cos(tan1)}, sin[cos{sin(tan1)}]]Correct answer is option 'A'. Can you explain this answer?.
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