1+sinα+cosα=2 * cos α/2*cos(π/4-α/2)α-альфа

Question

1+sinα+cosα=2 * cos α/2*cos(π/4-α/2)

α-альфа

Answer 1

2√2*1/2*(cos(a/2-π/4+a/2)+cos(a/2+π/4-a/2))=
=√2(cos(a-π/4)+cosπ/4)=√2*(cosacosπ/4+sinasinπ/4)+√2*√2/2=
=√2*(√2/2*cosa+√/2*sina)+1=√2*√2/2(cosa+sina)+1=
=cosa+sina+1