tentukan hasil dari 4 sin 75° cos15°

Sin 75 cos 15 = sin(45+30) . cos (45-30)
= (sin45.cos30 + sin30.cos45) . (cos45cos30 + sin45sin30)
= (√2/2 . √3/2 + 1/2 . √2/2) . (√2/2 . √3/2 + √2/2 . 1/2)
= 2(√2/2 . √3/2 + 1/2 . √2/2)
= 2(√6/4 + √√2/4)
= 2((√6 + √2)/4)
= (√6 + √2)/2
= 1/2 √6 + 1/2 √2
= 1/2(√6 + √2)

4 sin 75°cos15° = 2×{2·sin75°cos15°}=2·{sin(75°+15°)+sin(75°-15°)}
                          = 2 {sin90°+sin60°}
                          = 2 { 1 +[tex] \frac{1}{2} \sqrt{3} [/tex]
                          = 2 + [tex] \sqrt{3} [/tex]