Calculate sin 15 + sin 75 = ?

[Math Tutor]

Calculate the following expression:
sin 15° + sin 75° = ?

[ivan9302]

Calculate the following expression:
sin 15° + sin 75° = ?

[tex]sin15=sin(45-30)=sin45.cos30-sin30.cos45[/tex]
[tex]sin75=sin(30+45)=sin30.cos45+sin45.cos30[/tex]

[tex]sin15=sin(45-30)=sin45.cos30-sin30.cos45=\frac{\sqrt{2} }{2 }.\frac{\sqrt{3} }{2 }-\frac{1}{2 }.\frac{\sqrt{2} }{2 }=\frac{\sqrt{6}-\sqrt{2} }{ 4}[/tex]

[tex]sin75=sin(30+45)=sin30.cos45+sin45.cos30=\frac{1}{2 }. \frac{\sqrt{2} }{2 }+\frac{\sqrt{2} }{ 2}.\frac{\sqrt{3} }{2 }=\frac{\sqrt{2}+\sqrt{6} }{4 }[/tex]

[tex]sin15+sin75=\frac{\sqrt{6}-\sqrt{2} }{ 4} +\frac{\sqrt{2}+\sqrt{6} }{4 }=\frac{2\sqrt{6} }{ 4} =\frac{\sqrt{6} }{2 }[/tex]

[Guest]

Calculate the following expression:
sin 15° + sin 75° = ?

[leesajohnson]

Sin15 + Sin75 = ?
Sin15 = 0.25881905
Sin75 = 0.96592583

=> 0.25881905 + 0.96592583 = 1.2247

[Vicenta]

Calculate the following expression:
sin 15° + sin 75° = ?

Solution:

sin15+sin75 = sin75+sin 15 = 2sin (75+15)/2 * cos (75-15)/2 = 2sin 45*cos30

=2 (1/sqrt2)*(sqrt3/2) = 2(sqrt2*sqrt3)/4 = (sqrt6)/2.

2nd metod to solve:

sin15 + sin75 = sin15+ sin (90 -15) = sin15+cos15 = {(1/sqrt2)sin15 + (1/sqrt2) cos 15}sqrt2

(sin45*sin15 + cos45cos15)sqrt2

= cos (45-15) sqrt2

= (cos 30 )sqrt2

= {(sqrt3)/2} sqrt2

= (sqrt6)/2