Tentukan nilai dari 2 cos 40° cos 20° - 2 sin 55° sin 35°

jawab

2 cos 40 cos 20 -  2 sin 55 sin 35
= cos (40+20) + cos (40-20)  -  {cos (55+35) - cos (55-35)}
= cos 60 - cos 20 - cos 90 + cos 20
= 1/2

cos a + cos b = 2 cos (a+b)/2 cos (a-b)/2
cos a - cos b = -2 sin (a+b)/2 sin (a-b)/2

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2 cos 40 cos 20 - 2 sin 55 sin 35
= cos (40+20) + cos (40-20) + cos (55+35) - cos (55 - 35)
= cos 60 + cos 20 + cos 90 - cos 20
= cos 60 + cos 90
= 1/2