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antontolstyh8
@antontolstyh8
July 2022
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Sin(pi/4+a )sin(pi/4-a)+sinквадрат a
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aleks41
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+sin²
α)=0,5·1=0,5.
Ответ: 0,5.
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Answers & Comments
=(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.