Verified answer

[tex] \ctg(15) = \frac{1}{ \tg(15) } \\ \tg( \frac{30}{2} ) = \frac{ \sin(30) }{1 + \cos(30) } = \frac{ \frac{1}{2} }{1 + \frac{ \sqrt{3} }{2} } = \\ \frac{ \frac{1}{2} }{ \frac{2 + \sqrt{3} }{2} } = \frac{1}{2 + \sqrt{3} } \\ \ctg(15) = \frac{1}{ \frac{1}{2 + \sqrt{3} } } = 2 + \sqrt{3} [/tex]

[tex]1 - \sin(60) = 1 - \frac{ \sqrt{3} }{2} [/tex]

[tex] \ctg(15) (1 - \sin(60) ) = (2 + \sqrt{3} )(1 - \frac{ \sqrt{3} }{2} ) = \\ 2 - \sqrt{3} + \sqrt{3 } - \frac{3}{2} = 2 - 1 \frac{1}{2} = \frac{1}{2} [/tex]

Ответ: D)