Question

State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) $sec A=\frac{12}{5}$ for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) $sin\Theta =\frac{4}{3}$ for some angle θ.

Answer 1

SOLUTION :  

(i) The value of tan A is always less than 1 : FALSE.

In the case of tan θ , the values increases from 0 to ∞,where 0 ≤ θ ≤ 90°.

tan A < 1

Value of tan A at 45° is  = 1

As value of A increases to 90°

tan A becomes infinite (∞)

Hence, this  given statement is FALSE.

(ii) sec A = 12/5 for some value of ∠A is  TRUE.

sec A = 12/5 for some value of angle if

sec A = 2.4

sec A > 1

Hence,  this given statements is TRUE.

(iii) Cos A is the abbreviation used for cosecant of angle A : FALSE

cos A is the abbreviation used for cosine of angle A , not as cosecant of angle A.

Hence , this given statement is FALSE.

 

(iv) Cot A is the product of cot A and A : FALSE

∵ cot A is a cotangent of angle A  

cotangent of angle A (cot A) = adjacent side/ Opposite Side = B/P

Hence , this given statement is FALSE.

(v) sin θ = 4/ 3 for some angle θ is FALSE.

As we know that the hypotenuse is the longest side in a right angle triangle , so the value of Sin A is always less than or equal to 1.

Here value of sin θ = 4/ 3 = 1.333... exceeds 1.

Hence , this given statement is FALSE

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Solution :

(i) False because sides of a right triangle may have  any length, so tan A may have any value.

(ii) True as sec A is always greater than 1.

(iii) False as cos A is the abbreviation used for cosine A.

(iv) False as cot A is not the product of 'cot' and A 'cot' separated from A has no meaning.

(v) False as sin Θ cannot be > 1.