Q.11) State whether the following are true or false. Justify your answer.

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

EXERCISE 8.1

tan A =

BC

AB

Justification:

tan A is not always less than 1.

Hence, the given statement is false.

∴

If BC < AB,

then tan A < 1

If BC = AB,

then tan A = 1

If BC > AB,

then tan A > 1

EXERCISE 8.1

Justification:

In a right angled triangle,

Hence, the given statement is true.

sec A

=

We know that hypotenuse is the longest side in a right angled triangle.

∴

sec A can never be less than 1.

sec A =

12

5

> 1

∴

sec A =

12

5

for some angle A.

Q.11) State whether the following are true or false. Justify your answer.

(iii) cos A is the abbreviation used for the cosecant of angle A.

EXERCISE 8.1

Justification:

cos A is the abbreviation used for cosine of ∠A.

Abbreviation used for cosecant of ∠A is cosec A.

Hence, the given statement is false.

Q.11) State whether the following are true or false. Justify your answer.

(iv) cot A is the product of cot and A.

EXERCISE 8.1

Justification:

cot A is not the product of ‘cot’ and ∠A.

‘cot’ separated from ∠A has no meaning.

Hence, the given statement is false.

EXERCISE 8.1

Justification:

In a right angled triangle,

Hence, the given statement is false.

Opposite side of θ

Hypotenuse

sin θ

=

But, hypotenuse is the longest side in a right angled triangle.

∴

sin θ can never be greater than 1.

sin θ =

4

3

> 1

∴

sin θ =

4

3

is not possible for any θ.