解決sin(x)*sin(x+pi/4)=1/4sqrt{2} |Microsoft數學求解器

$$\sin ( x ) \times \sin ( x+ \frac{ \pi }{ 4 } ) = \frac{ 1 }{ 4 \sqrt{ 2 } }$$

解 x (復數求解)

$$x=\frac{8\pi n_{1}+4\arctan(\sqrt{7})-\pi }{8}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{8\pi n_{2}-4\arctan(\sqrt{7})+7\pi }{8}\text{, }n_{2}\in \mathrm{Z}$$

解 x

$$x=\frac{8\pi n_{1}+4\arccos(\frac{\sqrt{2}}{4})-\pi }{8}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{8\pi n_{2}-4\arccos(\frac{\sqrt{2}}{4})+7\pi }{8}\text{, }n_{2}\in \mathrm{Z}$$