If sin θ = cos θ and 0° < θ <90°, then find the values of sin θ and cos θ.

Given: sinθ = cosθ

⇒ tan θ = 1

Let,

Side opposite to angle θ = AB =1k

The side adjacent to angle θ = BC =1k

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

⇒ (1k)² + (1k)² = (AC)²

⇒ (AC)² = 1k² +1k²

⇒ (AC)² = 2k²

⇒ AC =√2k²

⇒ AC =k√2

So, AC = k√2

Now, we will find the sin θ

Side opposite to angle θ = AB= 1k

and Hypotenuse = AC = k√2

So,

Now, we know that,

The side adjacent to angle θ = BC =1k

Hypotenuse = AC =k√2

So,