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The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x | is a) (2√2)-1 b) (2√2)+1 c) (√2)-1 d) (√2)+1 Correct answer is option 'a'. Can you explain this answer?
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The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x...
Solution:
To find the minimum value of | sin x cos x tan x sec x cosec x cot x |, we need to find the minimum value of each of the six trigonometric functions separately.
Minimum value of sin x:
The minimum value of sin x is -1, which occurs when x = -π/2.
Minimum value of cos x:
The minimum value of cos x is -1, which occurs when x = π.
Minimum value of tan x:
The minimum value of tan x is -∞, which occurs when x = -π/2 or x = π/2.
Minimum value of sec x:
The minimum value of sec x is -∞, which occurs when x = π/2 or x = -π/2.
Minimum value of cosec x:
The minimum value of cosec x is -∞, which occurs when x = π or x = 0.
Minimum value of cot x:
The minimum value of cot x is -∞, which occurs when x = π/2 or x = -π/2.
Since we are looking for the minimum value of the absolute value of these six trigonometric functions, we can ignore the negative signs and just consider the values themselves.
Therefore, the minimum value of | sin x cos x tan x sec x cosec x cot x | is:
| sin x cos x tan x sec x cosec x cot x | = |sin x| |cos x| |tan x| |sec x| |cosec x| |cot x|
= (1) (1) (−∞) (−∞) (−∞) (−∞)
= ∞
However, we need to take into account that the question asks for the minimum value of the absolute value of these six trigonometric functions, which means that the answer cannot be ∞.
To solve this problem, we need to find the minimum value of the product of the absolute values of these six trigonometric functions.
Minimum value of | sin x cos x tan x sec x cosec x cot x |:
| sin x cos x tan x sec x cosec x cot x | = |sin x| |cos x| |tan x| |sec x| |cosec x| |cot x|
= (1) (1) (|tan x|) (|sec x|) (|cosec x|) (|cot x|)
We can simplify this expression as follows:
| sin x cos x tan x sec x cosec x cot x | = |sin x cos x| |tan x sec x cosec x cot x|
= |sin 2x| |(sin x cos x)/(sin x cos x)|
= |sin 2x|
The minimum value of |sin 2x| is 0, which occurs when x = 0, π/2, π, or 3π/2.
Therefore, the minimum value of | sin x cos x tan x sec x cosec x cot x | is:
| sin x cos x tan x sec x cosec x cot x | = |sin 2x|
= 0
To find the minimum value of | sin x cos x tan x sec x cosec x cot x |, we need to find the minimum value of each of the six trigonometric functions separately.
Minimum value of sin x:
The minimum value of sin x is -1, which occurs when x = -π/2.
Minimum value of cos x:
The minimum value of cos x is -1, which occurs when x = π.
Minimum value of tan x:
The minimum value of tan x is -∞, which occurs when x = -π/2 or x = π/2.
Minimum value of sec x:
The minimum value of sec x is -∞, which occurs when x = π/2 or x = -π/2.
Minimum value of cosec x:
The minimum value of cosec x is -∞, which occurs when x = π or x = 0.
Minimum value of cot x:
The minimum value of cot x is -∞, which occurs when x = π/2 or x = -π/2.
Since we are looking for the minimum value of the absolute value of these six trigonometric functions, we can ignore the negative signs and just consider the values themselves.
Therefore, the minimum value of | sin x cos x tan x sec x cosec x cot x | is:
| sin x cos x tan x sec x cosec x cot x | = |sin x| |cos x| |tan x| |sec x| |cosec x| |cot x|
= (1) (1) (−∞) (−∞) (−∞) (−∞)
= ∞
However, we need to take into account that the question asks for the minimum value of the absolute value of these six trigonometric functions, which means that the answer cannot be ∞.
To solve this problem, we need to find the minimum value of the product of the absolute values of these six trigonometric functions.
Minimum value of | sin x cos x tan x sec x cosec x cot x |:
| sin x cos x tan x sec x cosec x cot x | = |sin x| |cos x| |tan x| |sec x| |cosec x| |cot x|
= (1) (1) (|tan x|) (|sec x|) (|cosec x|) (|cot x|)
We can simplify this expression as follows:
| sin x cos x tan x sec x cosec x cot x | = |sin x cos x| |tan x sec x cosec x cot x|
= |sin 2x| |(sin x cos x)/(sin x cos x)|
= |sin 2x|
The minimum value of |sin 2x| is 0, which occurs when x = 0, π/2, π, or 3π/2.
Therefore, the minimum value of | sin x cos x tan x sec x cosec x cot x | is:
| sin x cos x tan x sec x cosec x cot x | = |sin 2x|
= 0
Community Answer
The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x...
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The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x | is a) (2√2)-1 b) (2√2)+1 c) (√2)-1 d) (√2)+1 Correct answer is option 'a'. Can you explain this answer?
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The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x | is a) (2√2)-1 b) (2√2)+1 c) (√2)-1 d) (√2)+1 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 The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x | is a) (2√2)-1 b) (2√2)+1 c) (√2)-1 d) (√2)+1 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 The minimum value of | sin x + cos x + tan x + sec x + cosec x + cot x | is a) (2√2)-1 b) (2√2)+1 c) (√2)-1 d) (√2)+1 Correct answer is option 'a'. Can you explain this answer?.
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