s i n α + s i n β = 2 s i n α + β 2 c o s α − β 2 sin~α+sin~β=2sin\frac{α+β}{2}cos\frac{α-β}{2} sin α+sin β=2sin2α+βcos2α−β s i n α − s i n β = 2 s c o s α + β 2 s i n α − β 2 sin~α-sin~β=2scos\frac{α+β}{2}sin\frac{α-β}{2} sin α−sin β=2scos2α+βsin2α−β c o s α + c o s β = 2 c o s α + β 2 c o s α − β 2 cos~α+cos~β=2cos\frac{α+β}{2}cos\frac{α-β}{2} cos α+cos β=2cos2α+βcos2α−β c o s α − c o s β = − 2 s i n α + β 2 s i n α − β 2 cos~α-cos~β=-2sin\frac{α+β}{2}sin\frac{α-β}{2} cos α−cos β=−2sin2α+βsin2α−β t a n α + t a n β = s i n ( α + β ) c o s α c o s β tan~α+tan~β=\frac{sin(α+β)}{cos~αcos~β} tan α+tan β=cos αcos βsin(α+β) t a n α − t a n β = s i n ( α − β ) c o s α c o s β tan~α-tan~β=\frac{sin(α-β)}{cos~αcos~β} tan α−tan β=cos αcos βsin(α−β)
s i n a ∗ c s c a = 1 sin~a*csc~a=1 sin a∗csc a=1 ， c s c a = 1 s i n a csc~a=\frac{1}{sin~a} csc a=sin a1
c o s a ∗ s e c a = 1 cos~a*sec~a=1 cos a∗sec a=1， s e c a = 1 c o s a sec~a=\frac{1}{cos~a} sec a=cos a1
t a n a ∗ c o t a = 1 tan~a*cot~a=1 tan a∗cot a=1， c o t a = 1 t a n a cot~a=\frac{1}{tan~a} cot a=tan a1 s e c 2 a − t a n 2 a = 1 sec^2a-tan^2a=1 sec2a−tan2a=1， 1 + t a n 2 a = s e c 2 a 1+tan^2a=sec^2a 1+tan2a=sec2a， s e c 2 − 1 = t a n 2 a sec^2-1=tan^2a sec2−1=tan2a
c s c 2 a − c o t 2 a = 1 csc^2a-cot^2a=1 csc2a−cot2a=1， 1 + c o t 2 a = c s c 2 a 1+cot^2a=csc^2a 1+cot2a=csc2a， c s c 2 − 1 = c o t 2 a csc^2-1=cot^2a csc2−1=cot2a s i n 2 a = 2 s i n a c o s a sin~2a=2sin~acos~a sin 2a=2sin acos a， c o s 2 a = c o s 2 a − s i n 2 a = 1 − 2 s i n 2 a = 2 c o s 2 a − 1 cos~2a=cos^2a-sin^2a=1-2sin^2a=2cos^2a-1 cos 2a=cos2a−sin2a=1−2sin2a=2cos2a−1
s i n 3 a = − 4 s i n 3 a + 3 s i n a sin~3a=-4sin^3a+3sin~a sin 3a=−4sin3a+3sin a， c o s 3 a = 4 c o s 3 a − 3 c o s a cos~3a=4cos^3a-3cos~a cos 3a=4cos3a−3cos a 降幂公式 s i n 2 a = 1 2 ( 1 − c o s 2 a ) sin^2a=\frac{1}{2}(1-cos2a) sin2a=21(1−cos2a)， c o s 2 a = 1 2 ( 1 + c o s 2 a ) cos^2a=\frac{1}{2}(1+cos2a) cos2a=21(1+cos2a)
s i n 2 a 2 = 1 2 ( 1 − c o s a ) sin^2\frac{a}{2}=\frac{1}{2}(1-cosa) sin22a=21(1−cosa)， c o s 2 a 2 = 1 2 ( 1 + c o s a ) cos^2\frac{a}{2}=\frac{1}{2}(1+cosa) cos22a=21(1+cosa)
c s c x = 1 s i n x csc~x=\frac{1}{sin~x} csc x=sin x1
( c s c x ) ′ = − c s c x c o t x (csc~x)'=-csc~xcot~x (csc x)′=−csc xcot x s e c x = 1 c o s x sec~x=\frac{1}{cosx} sec x=cosx1
( s e c x ) ′ = s e c x t a n x (sec~x)'=sec~xtan~x (sec x)′=sec xtan x c o t x = c o s x s i n x cot~x=\frac{cos~x}{sin~x} cot x=sin xcos x
( c o t x ) ′ = − c s c 2 x (cot~x)'=-csc^2x (cot x)′=−csc2x t a n x = s i n x c o s x tan~x=\frac{sin~x}{cos~x} tan x=cos xsin x
( t a n x ) ′ = s e c 2 x (tan~x)'=sec^2x (tan x)′=sec2x
( a r c s i n x ) ′ = 1 1 − x 2 (arc~sinx)'=\frac{1}{1-x^2} (arc sinx)′=1−x21
( a r c c o s x ) ′ = − 1 1 − x 2 (arc~cosx)'=-\frac{1}{1-x^2} (arc cosx)′=−1−x21
( a r c t a n x ) ′ = 1 1 + x 2 (arc~tanx)'=\frac{1}{1+x^2} (arc tanx)′=1+x21
( a r c c o t x ) ′ = − 1 1 + x 2 (arc~cotx)'=-\frac{1}{1+x^2} (arc cotx)′=−1+x21
