Question

Sa se calculeze ecuația:
cos (x-π/2)=sin2x

Answer 1

cos(x)cos(π/2) + sin(x)sin(π/2) =2sin(x)cos(x)
cos(π/2)=0
sin(π/2)=1
sin(x)=2sin(x)cos(x)    ; 2sin(x)cos(x) - sin(x) =0
sin(x)[2cos(x) - 1] =0
 1)  sin(x) =0
x = $(-1)^{k} arcsin0 + k \pi$ unde k∈Z
2)    2cos(x) -1=0
cos(x) = 1/2
x= +- arccos1/2 + 2kπ = +- π/3 + 2kπ  unde k∈Z