Q. 315.0( 1 Vote )

If 2 tan θ = 1, find the value of .

Answer :

Given: 2 tan θ = 1



We know that,



Or



Let,


Side opposite to angle θ =AB = 1k


Side adjacent to angle θ =BC = 2k


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


(k)2 + (2k)2 = (AC)2


(AC)2 = k2+4k2


(AC)2 = 5k2


AC =5k2


AC =±k5


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


Now, we will find the sin θ and cos θ


We know that



Side adjacent to angle θ = BC = 2k


and Hypotenuse = AC = k√5


So,


And


Side adjacent to angle θ =AB = 1k


And Hypotenuse =AC = k√5


So,


Now,





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