Question

Prove geometrically cos(x+y)=cosx×cosy-sinx×siny and hence show that cos 2x=cos²x-sin²x​.​

Answer 1

NOTE:HEY FRIEND PLEASE KEEP FULL QUESTION WITH THIS QUESTION THERE IS ALSO A DIAGRAM PLEASE LOOK INTO THAT

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.

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

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Answer 2

Answer:

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