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Anny00001
@Anny00001
July 2022
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Докажите тождество:
sina+cosa=√2cos(a-π/4)
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Answers & Comments
Genek55
Используем формулу cos(x-y) = cosx*cosy+sinx*siny
sinα+cosα = √2cos(α-π/4) = √2*(cosα*cos(π/4)+sinα*sin(π/4)) = √2*(cosα*(√2/2)+sinα*(√2/2)) = √2*(√2/2)(cosα+sinα) = cosα+sinα
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Answers & Comments
sinα+cosα = √2cos(α-π/4) = √2*(cosα*cos(π/4)+sinα*sin(π/4)) = √2*(cosα*(√2/2)+sinα*(√2/2)) = √2*(√2/2)(cosα+sinα) = cosα+sinα