Question

Помогите пожалуйстааааааааааааа

Answer 1

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

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

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)

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