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

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 = $\frac{12}{5}$ 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 $\theta$.

(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 = $\frac{12}{5}$

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 = $\frac{12}{5}$

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 $\theta=\frac{4}{3}$

sin $\theta$ = (Side Opposite to Angle A) / (Hypotenuse) = $\frac{4}{3}$

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.

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