Nilai eksak dari ( cos 2 0 ∘ cos 4 0 ∘ cos 8 0 ∘ ) adalah . . . .

Pembahasan

Ingat kembali bahwa: 2 cos A cos B = cos ( A + B ) + cos ( A – B ) cos A + cos B = cos ( 2 A + B ​ ) ⋅ cos ( 2 A − B ​ ) Sehingga diperoleh perhitungan: cos 2 0 ∘ cos 4 0 ∘ cos 8 0 ∘ = ( c os 2 0 ∘ cos 4 0 ∘ ) cos 8 0 ∘ = 2 1 ​ [ 2 cos 2 0 ∘ cos 4 0 ∘ ] cos 8 0 ∘ = 2 1 ​ [ [ cos ( 4 0 ∘ + 2 0 ∘ ) + cos ( 4 0 ∘ − 2 0 ∘ ] ⋅ cos 8 0 ∘ = 2 1 ​ [ cos 6 0 ∘ + cos 2 0 ∘ ] ⋅ cos 8 0 ∘ = 2 1 ​ [ 2 1 ​ + cos 2 0 ∘ ] ⋅ cos 8 0 ∘ = 2 1 ​ cos 8 0 ∘ ⋅ [ 2 1 ​ + cos 2 0 ∘ ] = 4 1 ​ cos 8 0 ∘ + 2 1 ​ cos 8 0 ∘ ⋅ cos 2 0 ∘ = 4 1 ​ cos 8 0 ∘ + 2 1 ​ ⋅ 2 1 ​ ⋅ ( 2 ⋅ cos 8 0 ∘ ⋅ cos 2 0 ∘ ) = 4 1 ​ cos 8 0 ∘ + 2 1 ​ ⋅ 2 1 ​ ⋅ [ cos ( 8 0 ∘ + 2 0 ∘ ) + cos ( 8 0 ∘ − 2 0 ∘ ) ] = 4 1 ​ cos 8 0 ∘ + 2 1 ​ ⋅ 2 1 ​ ⋅ [ cos 10 0 ∘ + cos 6 0 ∘ ] = 4 1 ​ cos 8 0 ∘ + 4 1 ​ ⋅ [ cos 10 0 ∘ + cos 6 0 ∘ ] = 4 1 ​ cos 8 0 ∘ + 4 1 ​ cos 10 0 ∘ + 4 1 ​ cos 6 0 ∘ = 4 1 ​ cos 8 0 ∘ + 4 1 ​ cos 10 0 ∘ + 4 1 ​ ⋅ 2 1 ​ = 4 1 ​ ( cos 8 0 ∘ + cos 10 0 ∘ ) + 8 1 ​ = 4 1 ​ ( cos ( 2 80 + 100 ​ ) ⋅ cos 2 100 − 8 0 ∘ ​ ) + 8 1 ​ = 4 1 ​ ( cos 90 ⋅ cos 10 ) + 8 1 ​ = 4 1 ​ ( 0 ⋅ cos 10 ) + 8 1 ​ = 8 1 ​ Dengan demikian, nilai dari ( cos 2 0 ∘ cos 4 0 ∘ cos 8 0 ∘ ) adalah ​ ​ 8 1 ​ ​ Jadi jawaban yang tepat adalah E.