Question

Review important identitie
cosx cosy = 1/2 [cos(x+y) + cos(x−y)]

Answer 1

`cosxcosy=(1)/(2)\left[cos(x+y)+cos(x-y)\right]\\\\R=(1)/(2)\left(cosxcosy-sinxsiny+cosxcosy-sinxsiny\right)\\\\=(1)/(2)\cdot2cosxcosy=cosxcosy=L\\\\R=L`

Answer 2

cos(x+y) = cosxcosy - sinxsiny;
cos(x-y) = cosxcosy + sinxsiny;
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=> cos(x+y) + cos(x-y) = 2cosxcosy =>cosx cosy = 1/2 [cos(x+y) + cos(x−y)];