If , find the value of 1+ cos² θ.

We know that,

Or

Let,

Side opposite to angle θ =AB = 8k

Side adjacent to angle θ =BC = 15k

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

⇒ (8k)² + (15k)² = (AC)²

⇒ (AC)² = 64k²+225k²

⇒ (AC)² = 289 k²

⇒ AC =√289 k²

⇒ AC =±17k

But side AC can’t be negative. So, AC = 17k

Now, we will find the cos θ

We know that

Side adjacent to angle θ = BC = 15k

and Hypotenuse = AC = 17k

So,

Now, we have to find the value of 1+ cos² θ

Putting the value of cos θ, we get