If find the value of cos θ – sin θ.

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