Q. 355.0( 2 Votes )

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

Answer :

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} = x^{2}+y^{2}

⇒ AC =√( x^{2}+y^{2})

Now, we will find the sin θ and cos θ

We know that

Side adjacent to angle θ = BC = y

and Hypotenuse = AC = √( x^{2}+y^{2})

So,

And

Side adjacent to angle θ =AB = x

And Hypotenuse =AC = √( x^{2}+y^{2})

So,

Now, x sin θ +y cos θ

= √( x^{2}+y^{2})

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