If , evaluate

(i)

(ii)

Given:

We know that,

Or

Let,

Side adjacent to angle θ =AB = 7k

Side opposite to angle θ =BC = 8k

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

⇒ (7k)² + (8k)² = (AC)²

⇒ (AC)² = 49 k² +69 k²

⇒ (AC)² = 113 k²

⇒ AC =√113 k²

⇒ AC =k√113

(i)

We know that,

(a+b)(a – b) = (a² – b²)

So, using this identity, we get

(ii) cot² θ

Given