sin105derajat x sin 15 derajat adalah

sin 105° × sin 15° = sin (45+60) × sin (45-30)
                     = (sin 45 cos 60 + cos 45 sin 60) × (sin 45 cos 30 - cos 45 sin 30)
                     = ([tex] \frac{1}{2} \sqrt{2} [/tex] × [tex] \frac{1}{2} [/tex] + [tex] \frac{1}{2} \sqrt{2} × \frac{1}{2} \sqrt{3} [/tex]) × ( [tex] \frac{1}{2} \sqrt{2} × \frac{1}{2} \sqrt{3} [/tex] - [tex] \frac{1}{2} \sqrt{2} [/tex] × [tex] \frac{1}{2} [/tex])
                      = ([tex] \frac{1}{4} \sqrt{2} + \frac{1}{4} \sqrt{6} [/tex]) × ([tex] \frac{1}{4} \sqrt{6} - \frac{1}{4} \sqrt{2} [/tex])
                      = -[tex] \frac{2}{16} + \frac{6}{16} [/tex]
                      = [tex] \frac{1}{4} [/tex]

Trogonometri

sin 105 x sin 15
= [(√2 + √6) / 4] x [-(√2 - √6) / 4]
= [(√2 + √6)(√2 - √6)] / -(4 x 4)
= (2 - 6) / -16
= -4 / -16
= 1/4