[obm-l] Re: Calcular tg 9� - tg 27� - tg 63� +tg81�

["Igor Correia Oliveira" <basketboy_igor@xxxxxxxxxx>]

Opa, eis a resosta!!!

Calcule tg 9� - tg 27� - tg 63� + tg81�

N = tg 9� - tg 27� - tg 63� + tg81�
N = (tg9� + tg 81�) - (tg 27� + tg 63�)
N = [(sen9�/cos9�) + (sen81�)/(cos81�)] - [(sen27�/cos27�) +
(sen63�/cos63�)]
N = [(sen81�)*(cos9�) + (sen9�)*(cos81�)]/(cos9�)*(cos81�) -
[(sen63�)*(cos27�) + (sen27�)*(cos63�)]/(cos27�)*(cos63�)
* sen(a+b) = sen(a)*cos(b) + sen(b)*cos(a) =>
N = 1/(cos9�)*(cos81�) - 1/(cos27�)*(cos63�)
* cos(a)*cos(b) = [cos(a+b) + cos(a-b)]/2
N = 1/[(cos90� + cos72�)/2] + 1/[(cos90� + cos36�)/2]
N = 2/cos72� - 2/cos36�
N = [2*(cos36�) - 2*(cos72�)]/(cos36�)*(cos72�)
N = 2*(cos36� - cos72�)/(cos36�)*(cos72�)
* cos(a) - cos(b) = -2*sen[(a+b)/2]*sen[(a-b)/2] =>
N = 2*[-2*(sen54�)*sen(-18�)]/(cos36�)*(cos72�)
N = 4*sen(54�)*sen(18�)/cos(36�)*cos(72�)
* sen(x)=cos(90-x) =>
N = 4
 Logo, tg 9� - tg 27� - tg 63� + tg81� = 4

Ufa!!!

Igor Correia Oliveira

#Mathematike

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