Mathematics Exam > Mathematics Questions > Ifα satisfies the in equations x2-x-2&g...
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If α satisfies the in equations x2-x-2>0 then a value exists for
- a)sin-1 α
- b)sec-1 α
- c)cos-1 α
- d)none
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Ifα satisfies the in equations x2-x-2>0 then a value exists f...
Explanation:
Given Inequality:
x^2 - x - 2 > 0
Factoring the Inequality:
(x - 2)(x + 1) > 0
Finding Critical Points:
x = 2, x = -1
Interval Testing:
-1 < x="" />< />
Interval Solution:
x ∈ (-∞, -1) U (2, ∞)
Connection to Trigonometric Functions:
Since the value of α must lie within the interval (-∞, -1) U (2, ∞), the only trigonometric function that satisfies this condition is sec^-1(α).
Therefore, the correct answer is option B) sec^-1α.
Given Inequality:
x^2 - x - 2 > 0
Factoring the Inequality:
(x - 2)(x + 1) > 0
Finding Critical Points:
x = 2, x = -1
Interval Testing:
-1 < x="" />< />
Interval Solution:
x ∈ (-∞, -1) U (2, ∞)
Connection to Trigonometric Functions:
Since the value of α must lie within the interval (-∞, -1) U (2, ∞), the only trigonometric function that satisfies this condition is sec^-1(α).
Therefore, the correct answer is option B) sec^-1α.
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Ifα satisfies the in equations x2-x-2>0 then a value exists fora)sin-1αb)sec-1αc)cos-1αd)noneCorrect answer is option 'B'. Can you explain this answer?
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