Sin(pi/4+a )sin(pi/4-a)+sinквадрат a

Question

Sin(pi/4+a )sin(pi/4-a)+sinквадрат a

Answer 1

Sin(π/4+α)·sin(π/4-α)+sin²α=
=(sin45°·cosα+sinα·cosα)(sin45°·cosα-sinα·cos45°)+sin²α=
=(√2/2·cosα+√2/2·sinα)(√2/2·cosα-√2/2·sinα)+sin²α=
=0.5cos²α-0.5sin²α+sin²α=
=0.5cos²α+0.5sin²α=
=0.5(cos²α+sin²α)=0,5·1=0,5.
Ответ: 0,5.