化简cos(a+b)cos(a-b)+sin^2b

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化简cos(a+b)cos(a-b)+sin^2b

化简cos(a+b)cos(a-b)+sin^2b
化简cos(a+b)cos(a-b)+sin^2b

化简cos(a+b)cos(a-b)+sin^2b
cos(a+b)cos(a-b)+sin^2b
=(cosacosb-sinasinb)(cosacosb+sinasinb)+sin^2b
=cos^2acos^2b-sin^2asin^2b+sin^2b
=cos^2acos^2b+cos^2asin^2b
=cos^2a

原式=1/2(cos2a+cos2b)+1/2(1-cos2b)
=1/2cos2a+1/2
=cos^2a
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sin(a B)sin(B-y)-cos(a B)cos(y-B) =sin(a B)sin(B-y)-cos(a B)cos(B-y) =-cos(a B B-y) =-cos(a 2B-y) sin(a B