Q. 175.0( 5 Votes )

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

Answer :

Given : sin θ =√3cos θ

tan θ =√3

We know that,


and tan θ = √3


The side opposite to angle θ =AC = k√3

The 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 + (k√3)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 θ and cos θ

Side opposite to angle θ = AC = k√3

and Hypotenuse = BC = 2k


Now, we know that,

The side adjacent to angle θ = AB =1k

Hypotenuse = BC =2k


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