Докажите тождество: sina+cosa=√2cos(a-π/4)

Question

Докажите тождество:
sina+cosa=√2cos(a-π/4)

Answer 1

Sinα+Cosα=√2Cos(α-π/4)
√2Cos(α-π/4)= √2(CosαCosπ/4 + SinαSinπ/4) = √2(Cosα*√2/2 + Sinα*√2/2)=
=√2*√2/2(Cosα + Sinα) = Cosα +Sinα