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

Given : sin θ =√3cos θ

⇒ tan θ =√3

We know that,

Or

and tan θ = √3

Let,

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

So,

Now, we know that,

The side adjacent to angle θ = AB =1k

Hypotenuse = BC =2k

So,