If tan , then find the value of cos θ.

We know that,

Or

Let,

The side opposite to angle θ =BC = 5k

The side adjacent to angle θ =AB = 12k

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

⇒ (12k)² + (5k)² = (AC)²

⇒ (AC)² = 144 k² +25 k²

⇒ (AC)² = 169 k²

⇒ AC =√169 k²

⇒ AC =±13k

But side AC can’t be negative. So, AC = 13k

Now, We know that

Side adjacent to angle θ = AB = 12k

and Hypotenuse = AC = 13k

So,