Nilai sin 105 + cos 15,adalah

sin 105 + cos 15
= sin (60 + 45) + cos (45 - 30)
= (sin 60 cos 45 + cos 60 sin 45) + (cos 45 cos 30 + sin 45 sin 30)
= (1/2 √3 x 1/2 √2 + 1/2 x 1/2 √2) + (1/2 √2 x 1/2 √3 + 1/2 √2 x 1/2)
= 1/4 (√6 + √2) + 1/4 (√6 + √2)
= 1/2 (√6 + √2)

[tex]\sin(105)=\sin(135-30) \\ \sin(105)=\sin(135)\cos(-30)+\cos(135)\sin(-30) \\ \sin(105)= (\frac{ \sqrt{2}}{2})(\frac{ \sqrt{3}}{2})+(-\frac{ \sqrt{2}}{2})(-\frac{1}{2}) \\ \sin(105)= \frac{ \sqrt{6}}{4}+\frac{ \sqrt{2}}{4} \\ \\ \sin(105)=\dfrac{ \sqrt{6}+ \sqrt{2}}{4}[/tex]

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

Jadi, 
[tex]\sin(105)+\cos(15)=\dfrac{ \sqrt{6}+ \sqrt{2}}{4}+\dfrac{ \sqrt{6}+ \sqrt{2}}{4} \\ \\ \sin(105)+\cos(15)=\dfrac{2\sqrt{6}+2\sqrt{2}}{4}[/tex]

[tex]\sin(105)+\cos(15)=\dfrac{\sqrt{6}+\sqrt{2}}{2}[/tex]