Which of the following statements are true?1) The value of tan A is always less than 1.2) sec A = 12 5 ,for some value of angle A.3) cos A is the abbreviation used for the cosecant of angle A.4) cot A is the product of cot and A.5) sin θ = 4 3 ,for some angle θ .

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Which of the following statements are true?

1) The value of tan A is always less than 1.

2) sec A = $125$ ,for some value of angle A.

3) cos A is the abbreviation used for the cosecant of angle A.

4) cot A is the product of cot and A.

5) sin θ = $43$ ,for some angle $θ$ .

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1,3,5

2,4

1,2,4

answer is C.

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Detailed Solution

Given, the value of tan A is always less than 1.
The range of the function f(x) = tan(x) is from negative infinity to positive infinity.
This means that it can have any real value.
So, statement 1 is false.
Given, sec A =

125

,for some value of angle A.
The range of the function f(x) = sec(x) is

(− ∞, − 1) ∪ (1, ∞)

. So, for some value of ‘A’, it can have the value

125

.
Hence, statement 2 is true.
Given, cos A is the abbreviation used for the cosecant of angle A.
cos(x) is the abbreviation for cosine(x), not cosecant(x).
So, statement 3 is false.
Given, cot A is the product of cot and A.
cot(A) is the abbreviation of cotangent(A).
So, statement 4 is false.
sin θ =