Q. 24 B3.6( 9 Votes )

If find the value of cos θ – sin θ.

Answer :

Given: sin θ =√3cos θ


tan θ = 3



We know that,



Or


Given: tan θ = √3




Let,


Side opposite to angle θ =AC = √3k


Side adjacent to angle θ =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 θ = AC = k√3


and Hypotenuse = BC = 2k


So,


Now, we know that,



The side adjacent to angle θ = AB =1k


Hypotenuse = BC =2k


So,


Now, we have to find the value of cos θ – sin θ


Putting the values of sin θ and cos θ, we get



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