Class 11 Exam > Class 11 Questions > The function cot(sinx) - (A) is not defined f...
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The function cot(sinx) -
(A) is not defined for x = (4n + 1)π/2
(B) is not defined for x = nπ
(C) lies between -cot 1 and cot 1
(D) can't lie between -cot 1 and cot 1.
Correct answer is option (B) and (D). Can you explain?
(A) is not defined for x = (4n + 1)π/2
(B) is not defined for x = nπ
(C) lies between -cot 1 and cot 1
(D) can't lie between -cot 1 and cot 1.
Correct answer is option (B) and (D). Can you explain?
Most Upvoted Answer
The function cot(sinx) - (A) is not defined for x = (4n + 1)π/2(B) is ...
Explanation:
The function is cot(sinx). Let's analyze the given options one by one.
Option (A):
The function cot(sinx) is defined for all x except where sinx = 0. So, for x = (4n+1)π/2, sinx = ±1 which means cot(sinx) is not defined for x = (4n+1)π/2. Hence, option (A) is incorrect.
Option (B):
For x = nπ, sinx = 0 which means cot(sinx) is not defined at these points. Hence, option (B) is correct.
Option (C):
The range of cot(x) is (-∞, ∞) except at x = nπ where it is undefined. So, the range of cot(sinx) will be (-∞, -cot1] ∪ [cot1, ∞). Hence, option (C) is incorrect.
Option (D):
As we have seen in option (C), the range of cot(sinx) is (-∞, -cot1] ∪ [cot1, ∞). So, it cannot lie between -cot1 and cot1. Hence, option (D) is correct.
Therefore, the correct options are (B) and (D).
The function is cot(sinx). Let's analyze the given options one by one.
Option (A):
The function cot(sinx) is defined for all x except where sinx = 0. So, for x = (4n+1)π/2, sinx = ±1 which means cot(sinx) is not defined for x = (4n+1)π/2. Hence, option (A) is incorrect.
Option (B):
For x = nπ, sinx = 0 which means cot(sinx) is not defined at these points. Hence, option (B) is correct.
Option (C):
The range of cot(x) is (-∞, ∞) except at x = nπ where it is undefined. So, the range of cot(sinx) will be (-∞, -cot1] ∪ [cot1, ∞). Hence, option (C) is incorrect.
Option (D):
As we have seen in option (C), the range of cot(sinx) is (-∞, -cot1] ∪ [cot1, ∞). So, it cannot lie between -cot1 and cot1. Hence, option (D) is correct.
Therefore, the correct options are (B) and (D).
Community Answer
The function cot(sinx) - (A) is not defined for x = (4n + 1)π/2(B) is ...
Cotx is undefined at the points where sinx is 0 so nπ
& since cotx is decreasing function so it lie between -infinity to -1 union 1 to infinity
& since cotx is decreasing function so it lie between -infinity to -1 union 1 to infinity
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The function cot(sinx) - (A) is not defined for x = (4n + 1)π/2(B) is not defined for x = nπ (C) lies between -cot 1 and cot 1 (D) can't lie between -cot 1 and cot 1.Correct answer is option (B) and (D). Can you explain?
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