If , prove that :

Given:

We know that,

Let,

BC = 4k and AC = 5k

where, k is any positive integer.

In right angled ∆ABC, we have

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

⇒ (AB)² + (4k)² = (5k )²

⇒ (AB)² + 16k² = 25k²

⇒ (AB)² = 25k² – 16k²

⇒ (AB)² = 9k²

⇒ AB = √9k²

⇒ AB =±3k [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

Now, RHS =

∴ LHS = RHS

Hence Proved