Question

((sin(п/4+a)-cos(п/4+a))/((sin(п/4+a)+cos(п/4+a)) -упростить

Answer 1

(sinπ/4*cosa-cosπ/4*sina)/[(sinπ/4*cosa+cosπ/4*sina)]=
=(√2/2*cosa-√2/2*sina)/(√2/2*cosa-√2/2*sina)=
=[√2/2*(cosa-sina)]/[√2/2*(cosa+sina)]=(cosa-sina)/(cosa+sina)=
[sin(π/2-a)-sina]/sin(π/2-a)+sina=2sin(π/4-a)cosπ/4/[2sinπ/4cos(π/4-a)]=
=[2*√2/2*sin(π/4-a)]/[2*√2/2*cos(π/4-a)]=tg(π/4-a)