# 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= 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) sinθ = 4/3 for some angle θ.

**Solution:**

(i) False, because tan 60^{°} = √3 > 1

(ii) sec A = hypotenuse / side adjacent to ∠Α

As hypotenuse is the largest side, the ratio on RHS will be greater than 1. Hence, the value of sec A is always greater than or equal to 1. Thus, the given statement is true.

(iii) Abbreviation used for cosecant of ∠A is cosec A and cos A is the abbreviation used for cosine of ∠A. Hence the given statement is false.

(iv) cot A is not the product of cot and A. It is the cotangent of ∠A. Hence, the given statement is false.

(v) We know that in a right-angled triangle, sin θ = side adjacent to ∠θ / hypotenuse

In a right-angled triangle, the hypotenuse is always greater than the remaining two sides. Also, the value of sine cannot be greater than 1 but 4/3 is > 1. Therefore, such a value of sin θ is not possible. Hence the given statement is false.

**Video Solution:**

## 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= 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) sinθ = 4/3 for some angle θ.

### Maths NCERT Solutions Class 10 - Chapter 8 Exercise 8.1 Question 11:

**Summary:**

For the following true and false questions: (i) The value of tan A is always less than - False, (ii) sec A= 12/5 for some value of angle A - True, (iii) cos A is the abbreviation used for the cosecant of an angle - False, (iv) cot A is the product of cot and - False, (v) sinθ = 4/3, for some angle θ - False.