Question

prove geometrically cos(x-y)=cosx cosy - sinx siny and hence deduce that 1)cos(x-y) 2)sin(x+y) 3)sin (x- y)

please answer me ​

Answer 1

Step-by-step explanation:

Let us take a circle of radius one and let us take 2 points P and Q such that P is at an angle x and Q at an angle y

as shown in the diagram

Therefore, the co-ordinates of P and Q are P(cosx,sinx),Q(cosy,siny)

Now the distance between P and Q is:

(PQ) 2=(cosx−cosy) 2+(sinx−siny) 2

=2−2(cosx.cosy+sinx.siny)

Now the distance between P and Q u\sin g \cos ine formula is

(PQ) 2 =1 2+1 2 −2cos(x−y)=2−2cos(x−y)

Comparing both we get

cos(x−y)=cos(x)cos(y)+sin(x)sin(y)

Substituting y with −y we get

cos(x+y)=cosxcosy−sinxsiny

Answer 2

`=cos^2 x - sin^2 x`.

I hope it helps you

please see attachment