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darksector07
@darksector07
August 2022
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Помогите решить, применял свойство переодичности и не особо вышло
Упростить: 4 cos a/4 * cos 2pi+a/4 * cos 2pi+a/2
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Юленька194
Verified answer
Cos (2π+α/4) = cos(α/4)
cos (2π+α/2) = cos (α/2)
4 cos (a/4) * cos (2pi+a/4) * cos( 2pi+a/2) = 4 cos(α/4)* cos(α/4)*cos (α/2) = 4cos²(α/4)*cos (α/2) =2cos²(α/4)*cos (2*α/4) = 4cos²(α/4)(1-sin²(α/4))= 4cos²(α/4)- 4cos²(α/4)*sin²(α/4)= 4cos²(α/4) -sin²(α/2)
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Answers & Comments
Verified answer
Cos (2π+α/4) = cos(α/4)cos (2π+α/2) = cos (α/2)
4 cos (a/4) * cos (2pi+a/4) * cos( 2pi+a/2) = 4 cos(α/4)* cos(α/4)*cos (α/2) = 4cos²(α/4)*cos (α/2) =2cos²(α/4)*cos (2*α/4) = 4cos²(α/4)(1-sin²(α/4))= 4cos²(α/4)- 4cos²(α/4)*sin²(α/4)= 4cos²(α/4) -sin²(α/2)