Помогите доказать тождества:sin(п/4+а)-сos(п/4+а)=tga 2.sin(a-B)/tga-tgB=cosa*cosB

Question

Помогите доказать тождества:sin(п/4+а)-сos(п/4+а)=tga
2.sin(a-B)/tga-tgB=cosa*cosB

Answer 1

1
(sinπ/4cosa+cosπ/4sina-cosπ/4cosa+sinπ/4sina)/(sinπ/4cosa+cosπ/4sina+cosπ/4cosa-sinπ/4sina)=(√2/2cosa+√2/2sina-√2/2cosa+√2/2sina)/(2/2cosa+√2/2sina+√2/2cosa-√2/2sina)=(√2sina)/(√2cosa)=tga
2
(sinacosb-sinbcosa):(sina/cosb-sinb/cosb)=
=(sinacosb-sinbcosa)*cosacosb/(sinacosb-sinbcosa)=cosacosb