arcsin ⁡ ( x ) + arccos ⁡ ( x ) = π / 2 {\displaystyle \arcsin(x)+\arccos(x)=\pi /2\;} arctan ⁡ ( x ) + arccot ⁡ ( x ) = π / 2. {\displaystyle \arctan(x)+\operatorname {arccot}(x)=\pi /2.\;} arctan ⁡ ( x ) + arctan ⁡ ( 1 / x ) = { π / 2 , n e ^ ´ u   x > 0 − π / 2 , n e ^ ´ u   x < 0 . {\displaystyle \arctan(x)+\arctan(1/x)=\left\{{\begin{matrix}\pi /2,&{\mbox{n}}{\acute {\hat {\mbox{e}}}}{\mbox{u}}\ x>0\\-\pi /2,&{\mbox{n}}{\acute {\hat {\mbox{e}}}}{\mbox{u}}\ x<0\end{matrix}}\right..} arctan ⁡ ( x ) + arctan ⁡ ( y ) = arctan ⁡ ( x + y 1 − x y ) {\displaystyle \arctan(x)+\arctan(y)=\arctan \left({\frac {x+y}{1-xy}}\right)\;} arctan ⁡ ( x ) − arctan ⁡ ( y ) = arctan ⁡ ( x − y 1 + x y ) {\displaystyle \arctan(x)-\arctan(y)=\arctan \left({\frac {x-y}{1+xy}}\right)\;} sin ⁡ ( arccos ⁡ ( x ) ) = 1 − x 2 {\displaystyle \sin(\arccos(x))={\sqrt {1-x^{2}}}\,} cos ⁡ ( arcsin ⁡ ( x ) ) = 1 − x 2 {\displaystyle \cos(\arcsin(x))={\sqrt {1-x^{2}}}\,} sin ⁡ ( arctan ⁡ ( x ) ) = x 1 + x 2 {\displaystyle \sin(\arctan(x))={\frac {x}{\sqrt {1+x^{2}}}}} cos ⁡ ( arctan ⁡ ( x ) ) = 1 1 + x 2 {\displaystyle \cos(\arctan(x))={\frac {1}{\sqrt {1+x^{2}}}}} tan ⁡ ( arcsin ⁡ ( x ) ) = x 1 − x 2 {\displaystyle \tan(\arcsin(x))={\frac {x}{\sqrt {1-x^{2}}}}} tan ⁡ ( arccos ⁡ ( x ) ) = 1 − x 2 x {\displaystyle \tan(\arccos(x))={\frac {\sqrt {1-x^{2}}}{x}}}