Question

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

(a) The value of tan A is always less than 1.
(b) Sec A =12/5 for some value of angle A.
(c) Cos A is the abbreviation used for the cosecant of angle A.
(d) Sin θ  =4/3 for some angle θ .

Answer 1

(a) tan A <1
Value of tan A at 45° i.e., tan 45 = 1
As value of A increases to 90°
Tan A becomes infinite
So given statement is false.

We get a right angle Δle
Subtending 9i at B.
So, given statement is true

(c) Cos A is the abbreviation used for cosecant of angle A.
The given statement is false. ∴ Cos A is abbreviation used for cos of angle A but not for cosecant of angle A.

cot A is co-tangent of angle A and co-tangent of angle A = adjacent side/opposite side

(e) Sinθ =4/3 for some angle θ Given statement is false

Since value of sinθ is less than (or) equal to one. Here value of sinθ exceeds one, so given statement is false.