Answer :

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


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