等价无穷小代换
1−cosx=x2/2=secx−11−cosx=x2/2=secx−1
(1+bx)a−1=abx(1+bx)a−1=abx
求导
(tanx)′=sec2x(tanx)′=sec2x
(cotx)′=−csc2x(cotx)′=−csc2x
(secx)′=secxtanx(secx)′=secxtanx
(cscx)′=−cscxcotx(cscx)′=−cscxcotx
(arctanx)′=11+x2(arctanx)′=11+x2
(arccotx)′=−11+x2(arccotx)′=−11+x2
(arcsinx)′=11−x2√(arcsinx)′=11−x2
(arcsinx)′=−11−x2√(arcsinx)′=−11−x2
积化和差化积
sina+sinb=2sina+b2cosa−b2sina+sinb=2sina+b2cosa−b2
sina−sinb=2cosa+b2sina−b2sina−sinb=2cosa+b2sina−b2
cosa+cosb=2cosa+b2cos