Question

prove that 1 + cos (x-y) = 2 cos^2 [(x-y)/2]​

Answer 1

Step-by-step explanation:

(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

1+cos(x-y)=2cos^2{(x-y)/2}

Answer 2

$\huge\bold \red{answer}$

Prove that

1+cos(x-y)=2cos^2[(x-y)/2]

Solution:

LHS =1+cos(x-y)

=1+cos(x-y)-> (1)

RHS =2cos^2((x-y)/2)

=2cos^2((x-y)/2)-> (2)

from (1) and (2)

Result is not proved...