第13章 13.26

sin⁡3x+sin⁡(x+π2)=2sin⁡(2x+π4)cos⁡(x−π4)=2sin⁡(2x+π4)sin⁡(x+π4)=3sin⁡(x+π4)\sin 3x + \sin\left(x+\dfrac{\pi}{2}\right) = 2\sin\left(2x+\dfrac{\pi}{4}\right)\cos\left(x-\dfrac{\pi}{4}\right) = 2\sin\left(2x+\dfrac{\pi}{4}\right)\sin\left(x+\dfrac{\pi}{4}\right) = \sqrt{3}\sin\left(x+\dfrac{\pi}{4}\right)

sin⁡(x+π4)=0\sin\left(x+\dfrac{\pi}{4}\right) = 0 これから −π4+nπ-\dfrac{\pi}{4}+n\pi

sin⁡(x+π4)≠0\sin\left(x+\dfrac{\pi}{4}\right) \neq 0 のとき

sin⁡(2x+π4)=32\sin\left(2x+\dfrac{\pi}{4}\right) = \dfrac{\sqrt{3}}{2} これから π24+nπ\dfrac{\pi}{24}+n\pi、524π+nπ\dfrac{5}{24}\pi+n\pi

解説: r31bn1z