# State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1(ii) Secfor 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) for some angle θ

(i) Consider a ΔABC, right-angled at B

Tan A =

But > 1

Tan A > 1

So, Tan A < 1 is not always true

Hence, the given statement is false

(ii) Sec A =

Let AC be 12k, AB will be 5k, where k is a positive integer

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

(12k)2 = (5k)2 + BC2

144k2 = 25k2 + BC2

BC2 = 119k2

BC = 10.9k

It can be observed that for given two sides AC = 12k and AB = 5k,

BC should be such that,

AC - AB < BC < AC + AB

12k - 5k < BC < 12k + 5k

7k < BC < 17 k

However, BC = 10.9k. Clearly, such a triangle is possible and hence, such value of sec A is possible

Hence, the given statement is true

(iii) Abbreviation used for cosecant of angle A is cosec A. And Cos A is the abbreviation used for cosine of angle A

Hence, the given statement is false

(iv) Cot A is not the product of cot and A. It is the cotangent of A

Hence, the given statement is false

(v) sin θ =

In a right-angled triangle, hypotenuse is always greater than the remaining two sides. Therefore, such value of sin θ is not possible

Hence, the given statement is false

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trick to learn all Trigonometric Formulae28 mins
Champ Quiz | Trigger on Trigonometry47 mins
Champ Quiz | Trigonometry Important Questions33 mins
NCERT | Trigonometric Identities52 mins
NCERT | Imp. Qs. on Trigonometry42 mins
Champ Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFREE Class
Quiz | Imp. Qs. on Trigonometry41 mins
Basic Concept of Trigonometry43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Given calculate all other trigonometric ratios.

KC Sinha - Mathematics

If , evaluate

(i)

(ii)

KC Sinha - Mathematics