Question

Помогите пожалуйстааааааааааааа

Answer 1

$sin(105)=sin(60+45)=sin60cos45+sin45cos60=\dfrac{\sqrt{3}}{2} * \dfrac{\sqrt{2}}{2} +\dfrac{\sqrt{2}}{2}*\dfrac{1}{2} = \dfrac{\sqrt{6}+\sqrt{2}}{4} = \boxed {\dfrac{\sqrt{3}+1}{2 \sqrt{2}}}$

$cos(105)=cos(60+45)=cos60cos45-sin60sin45=\dfrac{1}{2} *\dfrac{\sqrt{2}}{2} - \dfrac{\sqrt{3}}{2} * \dfrac{\sqrt{2}}{2}= \\ \\ =\dfrac{\sqrt{2}-\sqrt{6}}{4} = \boxed{ \dfrac{1-\sqrt{3}}{2\sqrt{2}}}$

1)

$sin(\dfrac{\pi}{3}-a)-\dfrac{1}{2} sina=sin(\dfrac{\pi }{3})cosa -sinacos(\dfrac{\pi}{3} )-\dfrac{1}{2} sina=\\ \\ = \dfrac{\sqrt{3}}{2}cosa - \dfrac{1}{2}sina - \dfrac{1}{2}sina = \boxed {\dfrac{\sqrt{3}}{2} cosa - sina}$

2)

$sin63cos27+cos63sin27=sin(63+27)=sin 90 = \boxed {1}$