高数公式总结

等价无穷小代换

$1-cos x = x^2 / 2 = sec x - 1$
$(1 + b x)^a - 1 = a b x$

求导

$(tan x)' = sec ^2 x$
$(cot x)' = -csc ^ 2 x$

$(sec x)' = sec x tan x$
$(csc x)' = -csc x cot x$

$(arc tan x)' = \frac {1}{1+x^2}$
$(arc cot x)' = -\frac {1}{1+x^2}$

$(arc sin x)' = \frac {1}{\sqrt{1-x^2}}$
$(arc sin x)' = -\frac {1}{\sqrt{1-x^2}}$

积化和差化积

$sin a + sin b = 2 sin \frac{a+b}{2} cos \frac {a-b}{2}$
$sin a - sin b = 2 cos \frac{a+b}{2} sin \frac {a-b}{2}$
cosa+cosb=2cosa+b2cos