Question

Помогите решить уравнение 9cosx......

Answer 1

$displaysyle 9^{cosx}=9^{sinx}*3^{frac{2}{cosx}}\\displaysyle 3^{2cosx}=3^{2sinx}*3^{frac{2}{cosx}}\\3^{2cosx}=3^{2sinx+frac{2}{cosx}}\\2cosx=2sinx+frac{2}{cosx},,,,,|*cosx neq 0\\cos^2x=sinx*cosx+1\\cos^2x-sinx*cosx-1=0\\cos^2x-sinx*cosx-sin^2x-cos^2x=0\\sin^2x+sinx*cosx=0\\sinx(sinx+cosx)=0\\\ left[begin{array}{ccc}sinx=0\sinx+cosx=0,,|:cosx neq 0end{array}right= textgreater left[begin{array}{ccc}x=pi n;,,,nin Z\tgx+1=0end{array}right= textgreater$

$left[begin{array}{ccc}x=pi n;,,,nin Z\tgx=-1end{array}right= textgreater boxed{left[begin{array}{ccc}x=pi n;,,,nin Z\x=-frac{pi}4+pi n;,,,nin Zend{array}right}$