Nilai eksak dari ( sin 1 0 ∘ sin 5 0 ∘ sin 7 0 ∘ ) adalah . . . .

Pembahasan

Ingat kembali bahwa: 2 ⋅ sin A ⋅ cos B = sin ( A + B ) + sin ( A − B ) 2 ⋅ sin A ⋅ sin B = − ( cos ( A + B ) − cos ( A − B ) ) sin A + sin B = cos ( 2 A + B ​ ) ⋅ sin ( 2 A − B ​ ) Sehingga diperoleh perhitungan: ​ = = = = = = = = = = = = = = = = ​ sin 1 0 ∘ sin 5 0 ∘ sin 7 0 ∘ ( sin 1 0 ∘ sin 5 0 ∘ ) ⋅ sin 7 0 ∘ ( 2 1 ​ ⋅ [ 2 sin 1 0 ∘ sin 5 0 ∘ ] ) ⋅ sin 7 0 ∘ ( − 2 1 ​ ⋅ [ cos ( 5 0 ∘ + 1 0 ∘ ) − cos ( 5 0 ∘ − 1 0 ∘ ) ] ) ⋅ sin 7 0 ∘ − 2 1 ​ ⋅ sin 7 0 ∘ ⋅ ( cos 6 0 ∘ − cos 4 0 ∘ ) − 2 1 ​ ⋅ sin 7 0 ∘ ⋅ ( 2 1 ​ − cos 4 0 ∘ ) − 4 1 ​ ⋅ sin 7 0 ∘ + 2 1 ​ sin 7 0 ∘ ⋅ cos 4 0 ∘ − 4 1 ​ ⋅ sin 7 0 ∘ + 4 1 ​ ( 2 sin 7 0 ∘ ⋅ cos 4 0 ∘ ) − 4 1 ​ ⋅ sin 7 0 ∘ + 4 1 ​ ( sin ( 7 0 ∘ + 4 0 ∘ ) + sin ( 7 0 ∘ − 4 0 ∘ ) − 4 1 ​ ⋅ sin 7 0 ∘ + 4 1 ​ ( sin 11 0 ∘ + sin 3 0 ∘ ) − 4 1 ​ ⋅ sin 7 0 ∘ + 4 1 ​ ( sin 11 0 ∘ + 2 1 ​ ) − 4 1 ​ ⋅ sin 7 0 ∘ + 4 1 ​ sin 11 0 ∘ + 8 1 ​ 4 1 ​ ( sin 11 0 ∘ − sin 7 0 ∘ ) + 8 1 ​ 4 1 ​ ( cos 2 110 + 70 ​ ⋅ sin 2 110 − 70 ​ ) + 8 1 ​ 4 1 ​ ( cos 90 ⋅ sin 20 ) + 8 1 ​ 4 1 ​ ( 0 ⋅ sin 20 ) + 8 1 ​ 8 1 ​ ​ Dengan demikian, nilai dari ( sin 1 0 ∘ sin 5 0 ∘ sin 7 0 ∘ ) adalah ​ ​ 8 1 ​ ​ Jadi jawaban yang tepat adalah A.