Question 1137908
<pre>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°)

{{{(1/2)(-1/2)=-1-sqrt(3)/2}}}

{{{-1/4=-1-sqrt(3)/2}}}

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

Edwin</pre>