Question

Упростите выражение sin(30°+a)–cos(60°+a)/sin(30°+a)+cos(60°+a)

Answer 1

$\frac{Sin(30+ \alpha )-Cos(60+ \alpha )}{Sin(30+ \alpha )+Cos(60+ \alpha )} = \frac{Sin30Cos \alpha +Sin \alpha Cos30-Cos60Cos \alpha +Sin60Sin \alpha }{Sin30Cos \alpha +Sin \alpha Cos30+Cos60Cos \alpha -Sin60Sin \alpha }=$$\frac{ \frac{1}{2}Cos \alpha + \frac{ \sqrt{3} }{2}Sin \alpha - \frac{1}{2}Cos \alpha + \frac{ \sqrt{3} }{2}Sin \alpha }{ \frac{1}{2}Cos \alpha + \frac{ \sqrt{3} }{2}Sin \alpha + \frac{1}{2}Cos \alpha - \frac{ \sqrt{3} }{2}Sin \alpha }= \frac{2* \frac{ \sqrt{3} }{2}Sin \alpha }{2* \frac{1}{2}Cos \alpha }= \frac{ \sqrt{3}Sin \alpha }{Cos \alpha }= \sqrt{3}tg \alpha$

Answer 2

(sin30cosa+sinacos30-cos60cosa+sin60sina) /(sin30cosa+sinacos30+cos60cosa-sin60sina)=
=(1/2*cosa+√3/2*sina-1/2*cosa+√3/2*sina)/
/(1/2*cosa+√3/2*sina+1/2*cosa-√3/2*sina)=
=√3sina/cosa=√3tga