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