Math 3

Math 3

Trigonometry

Chapter 1

sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)= ( tanA+tanB)/ (1-tanAtanB)
tan(A+B)= (tanA-tanB)/ ( 1+tanAtanB)

Chapter 2

2sinAcosB=sin(A+B)+sin(A-B)

2cosAsinB=sin(A+B)-sin(A-B)

2cosAcosB=cos(A+B)+cos(A-B)

2sinAsinB=cos(A-B)+cos(A+B)

Chapter-3

Chapter-4

Chapter-5

Set Algebra

Derivation

if x is real number. then,

if f(-x)=f(x) then f(x) even function; when f(-x)= - f(x) then f(x) odd function

{\frac {d}{dx}}e^{x}=e^{x}.

{\frac {d}{dx}}a^{x}=a^{x}\ln(a).

{\frac {d}{dx}}\ln(x)={\frac {1}{x}},\qquad x>0.

{\frac {d}{dx}}\log _{a}(x)={\frac {1}{x\ln(a)}}.

{\frac {d}{dx}}\sin(x)=\cos(x).

{\frac {d}{dx}}\cos(x)=-\sin(x).

{\frac {d}{dx}}\tan(x)=\sec ^{2}(x)={\frac {1}{\cos ^{2}(x)}}=1+\tan ^{2}(x).

{\frac {d}{dx}}\arcsin(x)={\frac {1}{\sqrt {1-x^{2}}}},-1<x<1.

{\frac {d}{dx}}\arccos(x)=-{\frac {1}{\sqrt {1-x^{2}}}},-1<x<1.

{\frac {d}{dx}}\arctan(x)={\frac {1}{1+x^{2}}}

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if y=f(u) and u=ɸ(x) , then dy/dx=dy/du . du/dx

if y=f(t) and x=g(t),then

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Important

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