сколько будет sin(45+L), cos(45+ L), cos3L, sin3L.. Created by Artem32481. algebra-ru

сколько будет sin(45+L), cos(45+ L), cos3L, sin3L...

July 2022 1 5 Report

сколько будет sin(45+L), cos(45+ L), cos3L, sin3L.

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iknowthatyoufeelbro 1) sin(45°+L)=sin(45°)*cos(L)+cos(45°)*sin(L)=√2/2*sin(L)+√2/2*cos(L)
2) cos(45°+L)=cos(45°)*cos(L)-sin(45°)*sin(L)=√2/2*cos(L)-√2/2*sin(L)
3) cos(3L) = cos(L)*cos(2L)-sin(L)*sin(2L) = cos(L)*(2cos²(L)-1)-sin(L)*2sin(L)*cos(L) = 2cos³(L)-cos(L)-2cos(L)*sin²(L) = 2cos³(L)-cos(L)-2cos(L)*(1-cos²(L)) = 2cos³(L)-cos(L)-2cos(L)+2cos³(L) = 4cos³(L)-3cos(L)
4) sin(3L) = sin(L)*cos(2L)+sin(2L)*cos(L) = sin(L)*(1-2sin²(L))+2sin(L)*cos(L)*cos(L) = sin(L)-2sin³(L)+2sin(L)*cos²(L) = sin(L)-2sin³(L)+2sin(L)*(1-sin²(L)) = sin(L)-2sin³(L)+2sin(L)-2sin³(L)=3sin(L)-4sin³(L)

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