Question

rozwiaz rownanie: dla x∈<0,2π>

Answer 1

2 cos ^2 (  3x - pi/4 ) = 1

2 cos^2 ( 3x - pi/4 ) - 1 = 0

Korzystam z wzoru

cos 2 alfa = 2 cos^2 alfa  - 1

zatem

cos [ 2*( 3x - pi/ 4)] = 0

cos ( 6x - pi/2 ) = 0

6x - pi/2 = pi/2  + 2 pi*k         lub     6x - pi/2 = (3/2) pi + 2 pi * k

6x = pi + 2 pi*k                       lub     6x = 2 pi + 2 pi *k

x = pi/6 + (pi/3)*k                  lub       x = pi/3 + ( pi/3)*k

k = 0,1,2,3,4,5  ....................... ...   k = -1, 0,1,2,3,4,5

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