Question

sin2x-cosx=2sinx-1

 

помогите!

Answer 1

$sin2x-cosx=2sinx-1$
$2six*cosx-cosx-2sinx+1=0$
$2sinx(cosx-1)-(cosx-1)=0$
$(cosx-1)(2sinx-1)=0$

$left[begin{array}{ccc}cosx-1=0\2sinx-1=0end{array}right= textgreater left[begin{array}{ccc}cosx=1\sinx=frac 12end{array}right= textgreater left[begin{array}{ccc}x=2pi n;nin Z\x=frac{pi}6+2pi n;nin Z\x=frac{5pi}6+2pi nnin Zend{array}right$