# If 4cot θ = 3, show that .

Given: cot θ

We know that,

Or

Let,

Side adjacent to angle θ =AB = 3k

The side opposite to angle θ =BC = 4k

where k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

(AB)2 + (BC)2 = (AC)2

(3k)2 + (4k)2 = (AC)2

(AC)2 = 9k2 +16k2

(AC)2 = 25k2

AC =25k2

AC =±5k

But side AC can’t be negative. So, AC = 5k

Now, we will find the sin θ

Side opposite to angle θ = BC = 4k

and Hypotenuse = AC = 5k

So,

Now, we know that,

Side adjacent to angle θ = AB =3k

Hypotenuse = AC =5k

So,

Now, LHS

= 7 = RHS

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Identities33 mins
Champ Quiz | Trigonometric Identities33 mins
NCERT | Trigonometric Identities52 mins
Quiz | Task on Trigonometric Ratios46 mins
Algebraic Identities48 mins
Quiz | Practice Important Questions on Trigonometrical Identities46 mins
Quiz on Trigonometric Ratios31 mins
T- Ratios of Specified Angles58 mins
Trick to learn all Trigonometric Formulae28 mins
Testing the T- Ratios of Specified Angles57 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