Question

VA ROOOG MUUULT!
1.Dacă tg u=3,calculați E=(sin u +2sin 3u+sin 5u)/(cos u+2 cos3u-cos 5u).

2.Daca tg x/2=3,calculați A=1/(sin x+ cos x) si B=1/(2+3cos x).

Answer 1

Răspuns:

Explicație pas cu pas:

1)   Se calc  R = (3^2+1^2)^0.5= r10

sin u = 3/r10

cos u =1/r10

sin 2u = 2*(3/r10)*(1/r10) = 0.6

cos 2u = 1/10-3/10= -2/10=-0.2

sin (2u+u) = 0.6*(1/r10)-(3/r10)*0.2=0.6/r10-0.6/r10=0

cos (2u+u) = -0.2*(1/r10)-0.6*(3/r10) = -2/r10

sin (2u+3u) = 0.6*(-2/r10) + 0*0.2= -1.2/r10

cos (2u+3u) = -0.2*(-2/r10) -0.6*0= 0.4/r10

E = (3/r10+2*0-1.2/t10)/(-0.2-2*2/r10 - 0.4/r10)= -(0.83+0.36/r10)= -0.94

2)   R= r10

sin x/2= 3/10

cos x/2 = 1/r10

sin x = 0.6

cos x = -0.2

A= 1/(0.6-0.2) = 1/0.4=2.5

B=1/(2-3*0.2) = 1/0.4 =2.5