等價無窮小代換

1−cosx=x2/2=secx−1$1-cosx=x^2/2=secx-1$
(1+bx)a−1=abx$(1+bx{)}^a-1=abx$

求導

(tanx)′=sec2x$(tanx{)}^{\prime }=se{c}^{2}x$
(cotx)′=−csc2x$(cotx{)}^{\prime }=-cs{c}^{2}x$

(secx)′=secxtanx$(secx{)}^{\prime }=secxtanx$
(cscx)′=−cscxcotx$(cscx{)}^{\prime }=-cscxcotx$

(arctanx)′=11+x2$(arctanx{)}^{\prime }=\frac{1}{1+x^2}$
(arccotx)′=−11+x2$(arccotx{)}^{\prime }=-\frac{1}{1+x^2}$

(arcsinx)′=11−x2√$(arcsi$

積化和差化積

sina+sinb=2sina+b2cosa−b2$sina+sinb=2sin\frac{a+b}{2}cos\frac{a-b}{2}$
sina−sinb=2cosa+b2sina−b2$sina-sinb=2cos\frac{a+b}{2}sin\frac{a-b}{2}$
cosa+cosb=2cosa+b2cosa−b2$cosa+cosb=2cos\frac{a+b}{2}cos\frac{a-b}{2}$
cosa−cosb=−2sina+b2sina−b2$cosa-cosb=-2sin\frac{a+b}{2}sin\frac{a-b}{2}$

sina∗sinb=−12[cos(a+b)−cos(a−b)