cos100^circ cdot cos32^circ cdot cos48^circ ... sin32^circ cdot sin48^circ leminin sonucu kactir?

Bu soruda, trigonometrik fonksiyonların çarpımı ve bölümü kullanarak sonucu bulmamız istenmektedir. Verilen ifadeyi adım adım çözelim:<br /><br />$cos100^{\circ} \cdot cos32^{\circ} \cdot cos48^{\circ} \cdot sin32^{\circ} \cdot sin48^{\circ}$<br /><br />Bu ifadeyi çözmek için, cos ve sin fonksiyonlarının çarpım ve bölüm özellikleri kullanılabileceğini fark edelim:<br /><br />$cos100^{\circ} \cdot cos32^{\circ} \cdot cos48^{\circ} \cdot sin32^{\circ} \cdot sin48^{\circ} = \frac{cos100^{\circ} \cdot cos32^{\circ} \cdot cos48^{\circ} \cdot sin32^{\circ} \cdot sin48^{\circ}}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot cos48^{\circ} \cdot sin48^{\circ}}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot cos(90^{\circ} - 32^{\circ}) \cdot sin(90^{\circ} - 32^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot sin58^{\circ} \cdot cos58^{\circ}}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} + sin(58^{\circ} - 100^{\circ}))}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin32^{\circ}}$<br /><br />$= \frac{cos100^{\circ} \cdot \frac{1}{2} \cdot (sin100^{\circ} - sin42^{\circ})}{cos32^{\circ} \cdot sin