Question

Помогите решить уравнение .

Answer 1

$\displaystyle\bf\\\Big(2Sinx-1\Big)\Big(3Sinx+1\Big)=0\\\\\\\left[\begin{array}{ccc}2Sinx-1=0\\3Sinx+1=0\end{array}\right\\\\\\\left[\begin{array}{ccc}2Sinx=1\\3Sinx=-1\end{array}\right\\\\\\\left[\begin{array}{ccc}Sinx=\dfrac{1}{2} \\Sinx=-\dfrac{1}{3} \end{array}\right\\\\\\\left[\begin{array}{ccc}x=\Big(-1\Big)^{n}arcSin\dfrac{1}{2} +\pi n,n\in Z \\x=\Big(-1\Big)^{n} arcSin\Big(-\dfrac{1}{3} \Big)+\pi n,n\in Z\end{array}\right$

$\displaystyle\bf\\\left[\begin{array}{ccc}x=\Big(-1\Big)^{n}\dfrac{\pi }{6} +\pi n,n\in Z \\x=\Big(-1\Big)^{n+1} arcSin\dfrac{1}{3}+\pi n,n\in Z\end{array}\right$