Rezolvați M=2|sinx|+cos2x

$$M = 2 | \sin x | + \cos 2 x$$

Rezolvați pentru M

$$M=2|\sin(x)|+\cos(2x)$$

Rezolvați pentru x

$$x=\pi +2\pi n_{2}+\left(-1\right)arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})\text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{84}\in \mathrm{Z}\text{ : }\left(not(\pi +2\pi n_{2}+\left(-1\right)arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})<2n_{84}\pi )\text{ and }not(\pi +2\pi n_{2}+\left(-1\right)arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})>\pi +2n_{84}\pi )\right)$$

$$x=arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }\exists n_{84}\in \mathrm{Z}\text{ : }\left(not(arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2\pi n_{1}<2n_{84}\pi )\text{ and }not(arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2\pi n_{1}>\pi +2n_{84}\pi )\right)$$

$$x=\pi +2\pi n_{29}+\left(-1\right)arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})\text{, }n_{29}\in \mathrm{Z}\text{, }\exists n_{84}\in \mathrm{Z}\text{ : }\left(not(\pi +2\pi n_{29}+\left(-1\right)arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})<2n_{84}\pi )\text{ and }not(\pi +2\pi n_{29}+\left(-1\right)arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})>\pi +2n_{84}\pi )\right)$$

$$x=arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2n_{28}\pi \text{, }n_{28}\in \mathrm{Z}\text{, }\exists n_{84}\in \mathrm{Z}\text{ : }\left(not(arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2n_{28}\pi <2n_{84}\pi )\text{ and }not(arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2n_{28}\pi >\pi +2n_{84}\pi )\right)$$

$$x=\pi +2\pi n_{106}+arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})\text{, }n_{106}\in \mathrm{Z}\text{, }not(SinI(\pi +2\pi n_{106}+arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}}))>0)$$

$$x=\left(-1\right)arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2\pi n_{105}\text{, }n_{105}\in \mathrm{Z}\text{, }not(SinI(\left(-1\right)arcSin(\frac{1}{2}+\left(-\frac{1}{2}\right)\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2\pi n_{105})>0)$$

$$x=\pi +2n_{108}\pi +arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})\text{, }n_{108}\in \mathrm{Z}\text{, }not(SinI(\pi +2n_{108}\pi +arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}}))>0)$$

$$x=\left(-1\right)arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2n_{353}\pi \text{, }n_{353}\in \mathrm{Z}\text{, }not(SinI(\left(-1\right)arcSin(\frac{1}{2}+\frac{1}{2}\left(3+\left(-2\right)M\right)^{\frac{1}{2}})+2n_{353}\pi )>0)$$