Question

cos^2 73 + cos^2 47 + cos47xcos73=k. Find k

Answer 1

$\huge\textbf{Solution}$
$<b>$
1/2[2cos^(47)+2cos^(73)+2cos(47)cos(73)]


=1/2[1+cos(94)+1+cos(146)+cos(120)+cos(26)]


=1/2[2+cos(94)+cos(146)-(1/2)+cos(26)]


=1/2[3/2+{cos(94)+cos(26)}+cos(146)]


=1/2[3/2+2cos(120)cos(34)+cos(146)]


=1/2[3/2+2(1/2)cos(34)+cos(146)]


=1/2[3/2+cos(34)+cos(146)]


=1/2[3/2+2cos(90)cos(56)]


=1/2[3/2+2(0).cos(56)]


=1/2[3/2+0]


=3/4


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