Tunjukan bahwa Cos (a+b) . cos (a-b) = (cos^2 a + cos^2 b) - 1
Matematika
calistacahyanin
Pertanyaan
Tunjukan bahwa Cos (a+b) . cos (a-b) = (cos^2 a + cos^2 b) - 1
1 Jawaban
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1. Jawaban MicoArrafi
[tex]$\begin{align}\cos(a+b)\cdot\cos(a-b)&=(\cos a\cos b-\sin a\sin b)(\cos a\cos b+\sin a\sin b)\\&=\cos^2a\cos^2b-\sin^2a\sin^2b\\&=\cos^2a(1-\sin^2b)-\sin^2b(1-\cos^2a)\\&=\cos^2a-\cos^2a\sin^2b-\sin^2b+\sin^2b\cos^2a\\&=\cos^2a-\sin^2b\\&=\cos^2a-(1-\cos^2b)\\&=\boxed{\cos^2a+\cos^2b-1}\ \bold{(terbukti)}\end[/tex]