Question

Find the valu of sin (15°)

Answer 1

let x = 15°

$we \: know \: that \\ \\ cos2x = 1 - 2 {sin}^{2} x \\ 2 {sin}^{2} x = 1 - cos2x \\ {sin}^{2} x = \frac{1 - cos2x}{2} \\ {sin}^{2} {15}^{o} = \frac{1 - cos {(2 \times 15)}^{o} }{2} = \frac{1 - cos {30}^{o} }{2} \\ {sin}^{2} {15}^{o} = \frac{1 - \frac{ \sqrt{3} }{2} }{2} = \frac{ \frac{2 - \sqrt{3} }{2} }{2} = ( \frac{2 - \sqrt{3} }{2} )( \frac{1}{2}) \\ {sin}^{2} {15}^{o} = \frac{2 - \sqrt{3} }{4} \\ \\ taking \: square \: roots \: on \: both \: sides \\ \\ sin {15}^{o} = \frac{ \sqrt{2 - \sqrt{3} } }{2}$