Answer :

Given: Sin θ


We know that,



Or



Let,


Perpendicular =AB =3k


and Hypotenuse =AC =5k


where, k is any positive integer


So, by Pythagoras theorem, we can find the third side of a triangle


In right angled ABC, we have


(AB)2 + (BC)2 = (AC)2


(3k)2 + (BC)2 = (5k)2


9k2 + (BC)2 = 25k2


(BC)2 = 25 k2 –9k2


(BC)2 = 16k2


BC =16k2


BC =±4k


But side BC can’t be negative. So, BC = 4k


Now, we have to find the value of cos θ and tan θ


We know that,



The side adjacent to angle θ or base = BC =4k


Hypotenuse = AC =5k


So,


Now,


We know that,




Perpendicular = AB =3k


Base = BC =4k


So,



Now, LHS






= RHS


Hence Proved


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