Question

cos2x=sinx+1 решить уровнение

Answer 1

cos2x=sinx+1
cos²x-sin²x=sinx+sin²x+cos²x
-sin²x=sinx+sin²x
2sin²x+sinx=0
sinx(2sinx+1)=0
a)sinx=0, x=k.π, k∈Z
b)2sinx+1=0,sinx=-1/2, x=7π/6+2k.π ili x=11π/6+2k.π, k∈Z

(sin(7π/6)=sin(11π/6)=-1/2)