Question

Sin x/2 + cosx = 1 (тригонометрические уравнения)

Answer 1

$Sin \frac{x}{2}+1-2Sin ^{2} \frac{x}{2} =1$
$Sin \frac{x}{2}-2Sin ^{2} \frac{x}{2}=0$
$Sin \frac{x}{2}(1-2Sin \frac{x}{2})= 0$
1) $Sin \frac{x}{2}=0$
$\frac{x}{2}= \pi n,n$∈z
$x= 2 \pi n,n$∈z
2) $1-2Sin \frac{x}{2}=0$
$2Sin \frac{x}{2} =1$
$Sin \frac{x}{2} = \frac{1}{2}$
$\frac{x}{2} = (-1) ^{n}arcSin \frac{1}{2}+ \pi n,n$∈z
$\frac{x}{2} =(-1) ^{n} \frac{ \pi }{6} + \pi n,n$∈z
$x=(-1) ^{n} \frac{ \pi }{3}+2 \pi n,n$∈z