Let us write with reason whether the following statements are true or false :

i. The value of tan A is always greater than 1.

ii. The value of cot A is always less than 1.

iii. For an angle θ, it may be possible that

iv. For an angle α, it may be possible that,

v. For an angle β (Beta) it may be possible that,

vi. For an angle θ, it may be possible that,

(i) TRUE

Let us consider ABC as a right angled triangle where ∠B = 90°

⇒

=

Let us assume that BC is greater than AB

Ex: BC = 6 and AB = 2

⇒

= 3

∴ tanA > 1

(ii) FALSE

Let us consider ABC as a right angled triangle where ∠B = 90°

⇒

=

Let us assume that AB is greater than BC

Ex: BC = 2 and AB = 8

⇒

= 4

∴ cotA > 1

(iii) FALSE

Given,

⇒ sinθ = 1.33

⇒ From the trigonometric ratios we know that sinθ value must lie between 0° to 90°

And sin90 = 1

(iv) FALSE

Given,

⇒ secα = 2.4

⇒ 2.4 does not lie between 0 and 2

(v) TRUE

Given,

⇒ cosecβ = 0.38

⇒ The value of cosec lie between 2 and 1

(vi) TRUE

Given,

⇒ cosθ = 0.6

⇒ The value of cos lie between 0 and 1, i.e 0° to 90°