**Trigonometric Ratios CBSE NCERT Solutions Chapter 8 Exercise 8.1 Question 11**

**11.** ** 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 = 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 for some angle .**

**(i)**

tan A = **(Side Opposite to Angle A) / (Side Adjacent to Angle A)**

Side Adjacent to Angle A can be equal to side opposite to angle A. Therefore, value of tan A can be equal to 1. Therefore, the given statement is **false**.

**(ii)**

sec A =

sec A = **(Hypotenuse) / (Side Adjacent to Angle A)**

As the length of the hypotenuse of triangle is always greater than the length of other two sides. So, it is possible that sec A =

Therefore, the given statement is** true**.

**(iii) **

cosec A is the abbreviation used for cosecant of angle A.

Therefore, the given statement is **false**.

**(iv)**

**False**

**(v) **

sin

sin = **(Side Opposite to Angle A) / (Hypotenuse)** =

It cannot be true because length of Hypotenuse cannot be smaller than length of any other side of triangle.

Therefore, the given statement is **false**.