12(cos(π2−3π4)−cos(π2+3π4))\frac{1}{2}\left(\cos\left(\frac{\pi}{2}-\frac{3\pi}{4}\right)-\cos\left(\frac{\pi}{2}+\frac{3\pi}{4}\right)\right)21(cos(2π−43π)−cos(2π+43π)) jika dituliskan dalam bentuk perkalian sinus menjadi ....
sinπ2sin3π4\sin\frac{\pi}{2}\sin\frac{3\pi}{4}sin2πsin43π
sin(−π4)sin5π4\sin\left(-\frac{\pi}{4}\right)\sin\frac{5\pi}{4}sin(−4π)sin45π
sinπ4sin5π4\sin\frac{\pi}{4}\sin\frac{5\pi}{4}sin4πsin45π
sinπ4sin(−5π4)\sin\frac{\pi}{4}\sin\left(-\frac{5\pi}{4}\right)sin4πsin(−45π)
sinπ2sin(−3π4)\sin\frac{\pi}{2}\sin\left(-\frac{3\pi}{4}\right)sin2πsin(−43π)
Rumus umum perkalian sinus adalah
sinαsinβ=12(cos(α−β)−cos(α+β))\sin\alpha\sin\beta=\frac{1}{2}\left(\cos\left(\alpha-\beta\right)-\cos\left(\alpha+\beta\right)\right)sinαsinβ=21(cos(α−β)−cos(α+β))
Dengan demikian,
12(cos(π2−3π4)−cos(π2+3π4))=sinπ2sin3π4\frac{1}{2}\left(\cos\left(\frac{\pi}{2}-\frac{3\pi}{4}\right)-\cos\left(\frac{\pi}{2}+\frac{3\pi}{4}\right)\right)=\sin\frac{\pi}{2}\sin\frac{3\pi}{4}21(cos(2π−43π)−cos(2π+43π))=sin2πsin43π