Question

Quiz Math
Level : Difficult


Nilai dari cos 10. cos 20. cos 40 . cos 50. cos 70. cos 80 adalah . Tentukan nilai dari a+b+c!

Mohon dengan cara!

Answer 1

Verified answer

Cos 10 cos 80
= 1/2 (cos 90 + cos 70)

cos 20 cos 70
= 1/2 (cos 90 + cos 50)

cos 40 cos 50
= 1/2 (cos 90 + cos 10)

...soal...
= 1/8 . cos 10 . cos 50 . cos 70
= 1/8 cos 10 . 1/2 . 2 cos 50 cos 70
= 1/16 cos 10 (cos 20 + cos 120)
= 1/16 cos 10 cos 20 - 1/32 cos 10
= 1/32 . 2 cos 10 cos 20 - 1/32 cos 10
= 1/32 (cos 10 + cos 30 - cos 10)
= 1/32 cos 30
= 1/64 √3
= a/b √c

a + b + c = 68