Question

which of the following is not true? *
A) -1 ≤ sinA ≤ 1
B) secA ≤ -1 OR secA ≥ 1
C) -1 ≤ cosA ≥ 1
D) -1 < cosec A < 1​

Answer 1

HELLO DEAR,

GIVEN:- Which of the following is not true?

A) -1 ≤ sinA ≤ 1

B) secA ≤ -1 OR secA ≥ 1

C) -1 ≤ cosA ≥ 1

D) -1 < cosec A < 1

ANSWER:-

Function Domain Range

sin ( x ) = (-∞ , + ∞) [-1 , 1]

cos ( x )= (-∞ , + ∞) [-1 , 1]

tan ( x )= All real numbers except (π/2 + n*π) (-∞, + ∞)

sec ( x )= All real numbers except (π/2 + n*π) (-∞ , -1] U [1 , + ∞)

cosec ( x )= All real numbers except (n*π) (-∞ , -1] U [1 , + ∞)

cot ( x )= All real numbers except (n*π) (-∞ , + ∞).

From above data it is clear that

C) -1 ≤ cosA ≥ 1 is not correct.

Because the range of cosA is [-1,1] and in (C) cosA≥1 is incorrect.

Therefore, right option is (C) -1 ≤ cosA ≥ 1.

THANKS.

Answer 2

Given :  

A) -1 ≤ sinA ≤ 1

B) secA ≤ -1 OR secA ≥ 1

C) -1 ≤ cosA ≤ 1  ( correction in Question)  

D) -1 < cosec A < 1​

To Find : Not  True statement

Solution:

Sin x  ∈ [-1, 1]

Cos x ∈ [-1 , 1}

Cosecx x =  1/sinx   ∈  R - (-1 , 1)

Secx = 1/cosx ∈  R - (-1 , 1)

tanx , cotx ∈ R

A) -1 ≤ sinA ≤ 1        TRUE

B) secA ≤ -1 OR secA ≥ 1  

TRUE

C) -1 ≤ cosA ≤ 1  ( correction in Question)

TRUE

D) -1 < cosec A < 1​

FALSE

as cosecA ≤ -1 OR cosecA ≥ 1     as cosecA   R - (-1 , 1)

Hence correct option is  D)  -1 < cosec A < 1​

as this is not TRUE.

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