cos(60+A)*cos(60-A)*cosA=1/1cos3A

Question

let"s check ypur mind

Comments

what a question har

Answer 1

I think you mean: cos(60-A)×cos(60+A)×cos(A)=¼cos(3A).

cos(60-A)=cos(A)/2+sin(A)√3/2;

cos(60+A)=cos(A)/2-sin(A)√3/2;

cos(60-A)cos(60+A)=cos²(A)/4-¾sin²(A).

cos(60-A)cos(60+A)cos(A)=cos³(A)/4-¾sin²(A)cos(A)=

cos³(A)/4-¾cos(A)+¾cos³(A)=cos³(A)-¾cos(A).

cos(3A)=cos(2A)cos(A)-sin(2A)sin(A)=

2cos³(A)-cos(A)-2sin²(A)cos(A)=

2cos³(A)-cos(A)-2(1-cos²(A))cos(A)=

2cos³(A)-cos(A)-2cos(A)+2cos³(A)=

4cos³(A)-3cos(A)=4(cos³(A)-¾cos(A)).

Therefore cos(3A)/4=cos(60-A)cos(60+A)cos(A) QED