If 2 tan θ = 1, find the value of .

Given: 2 tan θ = 1

We know that,

Or

Let,

Side opposite to angle θ =AB = 1k

Side adjacent to angle θ =BC = 2k

where, k is any positive integer

Firstly we have to find the value of AC.

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

⇒ (AB)² + (BC)² = (AC)²

⇒ (k)² + (2k)² = (AC)²

⇒ (AC)² = k²+4k²

⇒ (AC)² = 5k²

⇒ AC =√5k²

⇒ AC =±k√5

But side AC can’t be negative. So, AC = k√5

Now, we will find the sin θ and cos θ

We know that

Side adjacent to angle θ = BC = 2k

and Hypotenuse = AC = k√5

So,

And

Side adjacent to angle θ =AB = 1k

And Hypotenuse =AC = k√5

So,

Now,