Упростите выражение 1+sin2a+cos2a?

Question

Упростите выражение 1+sin2a+cos2a?

Answer 1

=cos²α+sin²α+2sinαcosα+cos²α-sin²α==2c0s²α+2sinαc0sα =2cosα(cosα+sinα)=

=2cosα(sin(π/2-α)+sinα)=2cosα·2sin(π/2-α+α)/2·cos(π/2-α-α)/2=

 =4cosα·sinπ/4·cos(π/4-α)=4cosα·√2/2·cos(π/4-α)=2√2cosα·cos(π/4-α)