If , show that =3.

Given:

We know that,

Let,

BC = 5k and AC = 13k

where, k is any positive integer.

In right angled ∆ABC, we have

(AB)² + (BC)² = (AC)² [by using Pythagoras theorem]

⇒ (AB)² + (5k)² = (13k )²

⇒ (AB)² + 25k² = 169k²

⇒ (AB)² = 169k² – 25k²

⇒ (AB)² = 144k²

⇒ AB = √144k²

⇒ AB =±12k [taking positive square root since, side cannot be negative]

Now, we have to find the value of other trigonometric ratios.

We, know that

Now, LHS =

=3 =RHS

Hence Proved