# Calculate sin 15 + sin 75 = ?

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Calculate sin 15 + sin 75 = ?

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

Math Tutor

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Joined: Sun Oct 09, 2005 11:37 am

### Re: Calculate sin 15 + sin 75 = ?

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

$sin15=sin(45-30)=sin45.cos30-sin30.cos45$
$sin75=sin(30+45)=sin30.cos45+sin45.cos30$

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

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

$sin15+sin75=\frac{\sqrt{6}-\sqrt{2} }{ 4} +\frac{\sqrt{2}+\sqrt{6} }{4 }=\frac{2\sqrt{6} }{ 4} =\frac{\sqrt{6} }{2 }$
ivan9302

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Joined: Mon May 03, 2010 2:56 pm

### Re: Calculate sin 15 + sin 75 = ?

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