If find the value of x sin θ + y cos θ.

We know that,

Or

Let,

Side opposite to angle θ =AB = x

Side adjacent to angle θ =BC = y

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

⇒ (x)² + (y)² = (AC)²

⇒ (AC)² = x²+y²

⇒ AC =√( x²+y²)

Now, we will find the sin θ and cos θ

We know that

Side adjacent to angle θ = BC = y

and Hypotenuse = AC = √( x²+y²)

So,

And

Side adjacent to angle θ =AB = x

And Hypotenuse =AC = √( x²+y²)

So,

Now, x sin θ +y cos θ

= √( x²+y²)