不邀自来

\arcsin(x+y) 是不能表示为 A\arcsin(x)+B\arcsin(y) 这种形式的，但是维基百科提供了下面这几组公式：

{\displaystyle \arcsin x+\arcsin y=\arcsin \left(x{\sqrt {1-y^{2}}}+y{\sqrt {1-x^{2}}}\right),xy\leq 0\lor x^{2}+y^{2}\leq 1} \\

{\displaystyle \arcsin x+\arcsin y=\pi -\arcsin \left(x{\sqrt {1-y^{2}}}+y{\sqrt {1-x^{2}}}\right),x>0,y>0,x^{2}+y^{2}>1}

{\displaystyle \arcsin x+\arcsin y=-\pi -\arcsin \left(x{\sqrt {1-y^{2}}}+y{\sqrt {1-x^{2}}}\right),x\arcsin x - \arcsin y = \pi - \arcsin\left(x\sqrt{1-y^2} - y\sqrt{1-x^2}\right), x > 0, y < 0, x^2 + y^2 > 1

\arcsin x - \arcsin y = - \pi - \arcsin\left(x\sqrt{1-y^2} + y\sqrt{1-x^2}\right), x < 0, y > 0, x^2 + y^2 > 1

\arccos x - \arccos y = -\arccos\left(xy + \sqrt{1-x^2}\cdot\sqrt{1-y^2}\right), x \geq y

\arccos x - \arccos y = \arccos\left(xy + \sqrt{1-x^2}\cdot\sqrt{1-y^2}\right), x < y

\arccos x - \arccos y = -\arccos\left(xy + \sqrt{1-x^2}\cdot\sqrt{1-y^2}\right), x \geq y

\arccos x - \arccos y = \arccos\left(xy + \sqrt{1-x^2}\cdot\sqrt{1-y^2}\right), x < y

\arctan\,x + \arctan\,y =\arctan\,{\frac{x+y}{1-xy}}, xy < 1

\arctan\,x + \arctan\,y =\pi + \arctan\,{\frac{x+y}{1-xy}}, x > 0, xy > 1

\arctan\,x + \arctan\,y =-\pi + \arctan\,{\frac{x+y}{1-xy}}, x < 0, xy > 1

\arctan x - \arctan y =\arctan{\frac{x-y}{1+xy}}, xy > -1

\arctan x - \arctan y =\pi + \arctan{\frac{x-y}{1+xy}}, x > 0, xy < -1

\arctan x - \arctan y =-\pi + \arctan {\frac{x-y}{1+xy}}, x < 0, xy < -1