Question

evaluate. sin (15/2)

Answer 1

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Answer 2

$cos \: 2 \alpha = 1 - 2{sin}^{2} \alpha \\ let \: 2 \alpha = 15 \\ \\ cos15 = 1 - 2 {sin}^{2} \frac{15}{2} \\ 2 {sin}^{2} \frac{15}{2} = 1 - cos(45 - 30) \\ 2 {sin}^{2} \frac{15}{2} = 1 - (cos45 \: cos30 + sin45 \: sin30) \\ 2 {sin}^{2} \frac{15}{2} = 1 - ( \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} ) \\ 2{sin}^{2} \frac{15}{2} = 1 - \frac{1}{2 \sqrt{2} } ( \sqrt{3} + 1) \\ {sin}^{2} \frac{15}{2} = \frac{2 \sqrt{2} - \sqrt{3} - 1 }{4 \sqrt{2} } \\ sin \frac{15}{2} = \sqrt{ \frac{ 2 \sqrt{2} - \sqrt{3} - 1}{4 \sqrt{2} } }$