SOLUTION: VERSIN(A+B)*VERSIN(A-B)

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Question 305799: VERSIN(A+B)*VERSIN(A-B)
Answer by Edwin McCravy(20086) About Me  (Show Source):
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VERSIN(A+B)*VERSIN(A-B)

[1-cos(A+B)][1-cos(A-B)]

1-cos(A-B)-cos(A+B)+cos(A+B)cos(A-B)

1-(cosAcosB+sinAsinB)-(cosAcosB-sinAsinB)+(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)

1-cosAcosB-sinAsinB-cosAcosB+sinAsinB+(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)

1-2cosAcosB+(cos²Acos²B-sin²Asin²B)

1-2cosAcosB+cos²Acos²B-sin²Asin²B

1-2cosAcosB+cos²Acos²B-(1-cos²A)(1-cos²B)

1-2cosAcosB+cos²Acos²B-(1-cos²B-cos²A+cos²Acos²B)

1-2cosAcosB+cos²Acos²B-1+cos²B+cos²A-cos²Acos²B

-2cosAcosB+cos²B+cos²A

cos²A-2cosAcosB+cos²B

(cosA-cosB)²

Edwin