Power operation 1. Multiplication of the same base power: a m ×a n =a (m+n).
2. power (a m) n = a (mn), product (ab) n = a nb n
3. Division of the same base power: a m÷÷an n = a (m-n).
4. Zero index: a 0 = 1.
Factorization formula (a+b)(a-b)=a? -B?
(A and B)? =a？ 2ab+b？
(a+b)(a？ -ab+b？ )=a？ +b？
(a-b)(a？ +ab+b？ )=a？ -B?
Answer? +b？ =(a+b)？ -2ab
(a-b)? =(a+b)？ -4ab
The trigonometric function half-angle formula sin(A/2)=√(( 1-cosA)/2)
sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)
cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))
tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
Sin2A=2SinA*CosA, the double-angle formula of trigonometric function
cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1
tan2A=(2tanA)/( 1-tanA^2)
Trigonometric function Trigonometric formula SIN3A = 4SINA * SIN (π/3+A) SIN (π/3-A)
cos3A = 4c OSA * cos(π/3+A)cos(π/3-A)
tan3A = tanA * tan(π/3+A)* tan(π/3-A)
The sum and difference formula of trigonometric function sin(A+B)=sinAcosB+cosAsinB.
sin(A-B)=sinAcosB-cossinB
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
Sum and difference of trigonometric function products Sinasinb =-[cos (a+b)-cos (a-b)]/2
cosAcosB=[cos(A+B)+cos(A-B)]/2
sinAcosB=[sin(A+B)+sin(A-B)]/2
cosAsinB=[sin(A+B)-sin(A-B)]/2
Trigonometric function and differential product sina+sinb = 2sin [(a+b)/2] cos [(a-b)/2]
sinA-sinB = 2cos[(A+B)/2]sin[(A-B)/2]
cosA+cosB = 2cos[(A+B)/2]cos[(A-B)/2]
cosA-cosB =-2 sin[(A+B)/2]sin[(A-B)/2]
tanA+tanB = sin(A+B)/cosa cosb = tan(A+B)( 1-tanA tanB)
tanA-tanB = sin(A-B)/cosa cosb = tan(A-B)( 1+tanA tanB)