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 =k2

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,

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