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 = 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)


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