გადაწყვიტეთ a=9sinxsinx

$$a = 9 \sin x \sin x$$

ამოხსნა x-ისთვის (complex solution)

$$x=\left(-i\right)\ln(\frac{1}{3}ia^{\frac{1}{2}}+\frac{1}{3}i\left(a-9\right)^{\frac{1}{2}})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

$$x=\left(-i\right)\ln(\frac{1}{3}ia^{\frac{1}{2}}+\left(-\frac{1}{3}i\right)\left(a-9\right)^{\frac{1}{2}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-i\right)\ln(\left(-\frac{1}{3}i\right)a^{\frac{1}{2}}+\frac{1}{3}i\left(a-9\right)^{\frac{1}{2}})+2\pi n_{14}\text{, }n_{14}\in \mathrm{Z}$$

$$x=\left(-i\right)\ln(\left(-\frac{1}{3}i\right)a^{\frac{1}{2}}+\left(-\frac{1}{3}i\right)\left(a-9\right)^{\frac{1}{2}})+2\pi n_{13}\text{, }n_{13}\in \mathrm{Z}$$

ამოხსნა a-ისთვის

$$a=9\left(\sin(x)\right)^{2}$$

ამოხსნა x-ისთვის

$$x=\arcsin(\frac{\sqrt{a}}{3})+\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\arcsin(\frac{\sqrt{a}}{3})+\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }a\geq 0\text{ and }a\leq 9$$