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
∴ LHS = RHS
Hence Proved
