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Jawaban terverifikasi

Jawaban

cos 15 0 ∘ ⋅ sin 21 0 ∘ − cos 6 0 ∘ = 2 1 ( 2 1 3 − 1 ) .

cos 15 0^{\circ} \cdot sin 21 0^{\circ} - cos 6 0^{\circ} = \frac{1}{2} (\frac{1}{2} 3 - 1)

Pembahasan

KIta gunakan sudut berelasi pada kuadran II dan kuadran III cos 15 0 ∘ ⋅ sin 21 0 ∘ − cos 6 0 ∘ = co s ( 18 0 ∘ − 3 0 ∘ ) ⋅ sin ( 18 0 ∘ + 3 0 ∘ ) − cos 6 0 ∘ = ( − cos 3 0 ∘ ) ( − sin 3 0 ∘ ) − cos 6 0 ∘ = − 2 1 3 ⋅ ( − 2 1 ) − ( 2 1 ) = 2 1 ( 2 1 3 − 1 ) Dengan demikian, cos 15 0 ∘ ⋅ sin 21 0 ∘ − cos 6 0 ∘ = 2 1 ( 2 1 3 − 1 ) .

KIta gunakan sudut berelasi pada kuadran II dan kuadran III

$cos 15 0^{\circ} \cdot sin 21 0^{\circ} - cos 6 0^{\circ} = co s (18 0^{\circ} - 3 0^{\circ}) \cdot sin (18 0^{\circ} + 3 0^{\circ}) - cos 6 0^{\circ} = (- cos 3 0^{\circ}) (- sin 3 0^{\circ}) - cos 6 0^{\circ} = - \frac{1}{2} 3 \cdot (- \frac{1}{2}) - (\frac{1}{2}) = \frac{1}{2} (\frac{1}{2} 3 - 1)$