SOLUTION: Prove: cos(𝛼 − 𝛽)cos(𝛼 + 𝛽) = cos2𝛼 − sin2𝛽

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Question 1137908: Prove: cos(𝛼 − 𝛽)cos(𝛼 + 𝛽) = cos2𝛼 − sin2𝛽
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
cos(𝛼 − 𝛽)cos(𝛼 + 𝛽) = cos2𝛼 − sin2𝛽

Sorry, that is false.  Let 𝛼=90° and 𝛽=30°

cos(90° − 30°)cos(90° + 30°) = cos[2(90°)] − sin[2(30°)]

cos(60°)cos(120°) = cos180° − sin(60°)

%281%2F2%29%28-1%2F2%29=-1-sqrt%283%29%2F2

-1%2F4=-1-sqrt%283%29%2F2

That's false for the left side is a rational number but the right side is
an irrational number.

Edwin