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JuliaKarma
@JuliaKarma
August 2022
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ТРИГОНОМЕТРИЯ
Упростить выражения:
а)[tex]4cos \frac{ \alpha }{4} *cos \frac{2 \pi + \alpha }{4} *cos \frac{2 \pi + \alpha }{2} [/tex]
б)[tex] \frac{1}{1-tg \alpha } - \frac{1}{1+tg \alpha } [/tex]
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vicper1957z
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sedinalana
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4cos(a/4)*cos(π/2+a/4)*cos(π+a/2)=4cos(a/4)*(-sin(a/4))*(-cos(a/2))=
=-2sin(a/2)*(-cos(a/2)=sina
1:(1-sina/cosa)-1:(1+sina/cosa)=cosa/(cosa-sina)-cosa/(cosa+sina)=
=cosa(cosa+sina-cosa+sina)/(cos²a-sin²a)=cosa*2sina/cos2a=
=sin2a/cos2a=tg2a
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Answers & Comments
Verified answer
.............................................................................................................Verified answer
4cos(a/4)*cos(π/2+a/4)*cos(π+a/2)=4cos(a/4)*(-sin(a/4))*(-cos(a/2))==-2sin(a/2)*(-cos(a/2)=sina
1:(1-sina/cosa)-1:(1+sina/cosa)=cosa/(cosa-sina)-cosa/(cosa+sina)=
=cosa(cosa+sina-cosa+sina)/(cos²a-sin²a)=cosa*2sina/cos2a=
=sin2a/cos2a=tg2a