Proszę wyjaśnić jeszcze dlaczego dochodze do sprzeczności upraszczając sin157 na dwa różne sposoby? Gdzie tu jest błąd? I. sin157=sin(180-23)=sin23=cos67 II. sin157=sin(90+67)=-cos67=-cos67
Janek191
Cos 315 = cos (360 - 45) = cos 45 sin 45 = cos 45 tg 135 = tg ( 90 + 45) = - ctg 45 = - 1 sin 240 = sin ( 180 + 60) = - sin 60 = - p(3)/2 sin^2 240 = [ - p(3)/2]^2 = 3/4
zatem sin 45 - cos 315 + tg 135*sin^2 240 = sin 45 - cos 45 - ctg 45*(3/4) = = - 1*( 3/4) = - 3/4 ================ sin 157 = sin ( 180 - 23) = sin 23 sin 157 = sin ( 90 + 67) = cos 67 = cos ( 90 - 23) = sin 23
sin 45 = cos 45
tg 135 = tg ( 90 + 45) = - ctg 45 = - 1
sin 240 = sin ( 180 + 60) = - sin 60 = - p(3)/2
sin^2 240 = [ - p(3)/2]^2 = 3/4
zatem
sin 45 - cos 315 + tg 135*sin^2 240 = sin 45 - cos 45 - ctg 45*(3/4) =
= - 1*( 3/4) = - 3/4
================
sin 157 = sin ( 180 - 23) = sin 23
sin 157 = sin ( 90 + 67) = cos 67 = cos ( 90 - 23) = sin 23
cos 315 = cos (180+135) = - cos 135 = -cos (180-45) = -(-cos 45) = cos 45 = V2/2
tg 135 = tg (90+45) = -ctg 45 = -1
sin 240 = sin (180+6) = - sin60 = -V3/2
sin^2 240 = (-V3/2)^2 = 3/4
sin 45 - cos 315 + tg 135 * sin^2 240 =
= V2/2 - V2/2 - 1 * 3/4 = -3/4
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sin 157 = sin (180-23) = sin 23
sin157 = sin (90+67) = cos 67 = cos (90-23) = sin 23