Q. 155.0( 3 Votes )

If tan B= √3, then find the values of sin B and cos B.

Answer :


We know that,



Or


Given: tan B = √3




Let,


Side opposite to angle B =AC = √3k


The side adjacent to angle B =AB = 1k


where k is any positive integer


Firstly we have to find the value of BC.


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


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


(1k)2 + (√3k)2 = (BC)2


(BC)2 = 1 k2 +3 k2


(BC)2 = 4 k2


BC =2 k2


BC =±2k


But side BC can’t be negative. So, BC = 2k


Now, we will find the sin B and cos B



Side opposite to angle B = AC = k√3


and Hypotenuse = BC = 2k


So,


Now, we know that,



The side adjacent to angle B = AB =1k


Hypotenuse = BC =2k


So,


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