좆간지나는 삼각함수 항등식

$$\begin{aligned} \sin(x+y+z) & =\sin x\cos y\cos z+\sin y\cos z\cos x+\sin z\cos x\cos y-\sin x\sin y\sin z \\ \cos(x+y+z) & =\cos x\cos y\cos z-\cos x\sin y\sin z-\sin x\cos y\sin z-\sin x\sin y\cos z \\ \tan(x+y+z) & =\dfrac{\tan x+\tan y+\tan z-\tan x\tan y\tan z}{1-\tan x\tan y-\tan y\tan z-\tan z\tan x} \end{aligned}$$

$$\begin{aligned} \sin x+\sin y+\sin z-\sin(x+y+z) & =4\sin\dfrac{x+y}{2}\sin\dfrac{y+z}{2}\sin\dfrac{z+x}{2} \\ \cos x+\cos y+\cos z+\cos(x+y+z) & =4\cos\dfrac{x+y}{2}\cos\dfrac{y+z}{2}\cos\dfrac{z+x}{2} \end{aligned}$$

$$\begin{aligned} \sin^2x-\sin^2y & =\sin(x+y)\sin(x-y)=\cos^2y-\cos^2x \\ \cos^2x-\sin^2y & =\cos(x+y)\cos(x-y)=\cos^2y-\sin^2x \end{aligned}$$

$$\begin{aligned} \sin x\sin(60^\circ-x)\sin(60^\circ+x) & =\dfrac{1}{4}\sin 3x \\ \cos x\cos(60^\circ-x)\cos(60^\circ+x) & =\dfrac{1}{4}\cos 3x \end{aligned}$$

$$\begin{aligned} \sin^2x+\sin^2(60^\circ-x)+\sin^2(60^\circ+x) & =\dfrac{3}{2} \\ \cos^2x+\cos^2(60^\circ-x)+\cos^2(60^\circ+x) & =\dfrac{3}{2} \end{aligned}$$

$$\begin{aligned} \cot x+\tan x & =2\csc 2x  \\ \cot x-\tan x & =2\cot 2x \end{aligned}$$

$$\sin^6x+\cos^6x=1+3\sin^2x\cos^2x$$

 

Exponential 17 김지하