Q. 373.7( 3 Votes )

If 4cot θ = 3, show that .

Answer :

Given: cot θ


We know that,



Or



Let,


Side adjacent to angle θ =AB = 3k


The side opposite to angle θ =BC = 4k


where k is any positive integer


Firstly we have to find the value of AC.


So, we can find the value of AC with the help of Pythagoras theorem


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


(3k)2 + (4k)2 = (AC)2


(AC)2 = 9k2 +16k2


(AC)2 = 25k2


AC =25k2


AC =±5k


But side AC can’t be negative. So, AC = 5k


Now, we will find the sin θ



Side opposite to angle θ = BC = 4k


and Hypotenuse = AC = 5k


So,


Now, we know that,



Side adjacent to angle θ = AB =3k


Hypotenuse = AC =5k


So,


Now, LHS




= 7 = RHS


Hence Proved


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