mathematics basic formulae

List of Basic Formulae in Mathematicsfor Students

M. D. Raghu

BASIC FORMULAE

FOR STUDENTSMATHEMATICS

©2014 MDR www.learningforknowledge.com/glg

𝒙𝒎 .𝒙𝒏=𝒙𝒎+𝒏

𝒙𝒎

𝒙𝒏 =𝒙𝒎−𝒏

(𝒙𝒎)𝒏=𝒙𝒎𝒏

𝒙𝒑𝒒=

𝒒√𝒙𝒑

Algebra

Indices Logarithms

log𝒃𝒙𝒚=log𝒃𝒙+ log𝒃𝒚

log𝒃𝒙𝒚= log𝑏𝒙− log𝒃 𝒚

log𝒃𝒙𝒏=𝒏 log𝒃𝒙

log𝒂𝒙=log𝑏𝒙log𝒃𝒂

BASIC FORMULAE



Arithmetic

𝒕𝒏=𝒂𝒓𝒏−𝟏

𝒓=𝒕𝒏𝒕𝒏−𝟏

Arithmetic Series

𝑎 ,𝑎+𝑑 ,𝑎+2𝑑 ,…Geometric Series

𝑎 ,𝑎𝑟 ,𝑎𝑟2 ,…

BASIC FORMULAE



Analytical Geomtery

Line Coordinates and Gradients

BASIC FORMULAE



Analytical Geomtery

Line Equations

BASIC FORMULAE



𝒔𝒊𝒏𝜽=𝒚𝒓

𝒄𝒐𝒔 𝜽=𝒙𝒓

𝒕𝒂𝒏𝜽=𝒚𝒙

𝒄𝒐𝒔𝒆𝒄 𝜽=𝒓𝒚

𝒔𝒆𝒄 𝜽=𝒓𝒙

𝒄𝒐𝒕 𝜽=𝒙𝒚

Trigonometry

Ratios

x

yr

θ

BASIC FORMULAE



cos−1 𝒙𝒓 =𝜽

sin−1 𝒚𝒓 =𝜽

tan−1 𝒚𝒙=𝜽 cot−1 𝒙𝒚=𝜽

c o se c−1 𝒓𝒚=𝜽

sec−1 𝒓𝒙=𝜽

Trigonometry

Inverse of Ratios

x

yr

θ

BASIC FORMULAE



tan𝜽=¿sin𝜽cos𝜽 ¿

tan2 θ + 1= sec2 θsin2 θ + cos2 θ = 1cosec 𝜽=

𝟏sin 𝜽

Trigonometry

Identities

sec𝜽=𝟏cos𝜽

cot 𝜽=cos𝜽sin 𝜽

cot2 θ + 1= cosec2 θtan θ × cot θ = 1

BASIC FORMULAE



Trigonometry

Products

2cos 𝐴 cos𝐵=cos (𝐴−𝐵 )+cos ( 𝐴+𝐵 )

2cos 𝐴 sin𝐵=sin ( 𝐴+𝐵 )− sin ( 𝐴−𝐵 )

2sin 𝐴 cos𝐵=sin ( 𝐴+𝐵 )+sin ( 𝐴−𝐵 )

2sin 𝐴sin 𝐵=cos ( 𝐴−𝐵 )− cos ( 𝐴+𝐵 )

BASIC FORMULAE



Trigonometry

Sums

cos𝐶+cos𝐷=2cos (𝐶+𝐷 )2

× cos (𝐶−𝐷 )2

sin𝐶−sin𝐷=2cos (𝐶+𝐷 )2

×sin (𝐶−𝐷 )2

cos𝐶− cos𝐷=−2sin (𝐶+𝐷 )2

×sin (𝐶−𝐷 )2

sin𝐶+sin𝐷=2sin (𝐶+𝐷 )2

×cos (𝐶−𝐷 )2

BASIC FORMULAE



tan ( 𝐴−𝐵 )= tan 𝐴− tan 𝐵1+ tan 𝐴 tan 𝐵

sin ( 𝐴−𝐵 )=sin 𝐴cos 𝐵− cos 𝐴 sin𝐵cos ( 𝐴+𝐵 )=cos 𝐴cos 𝐵− sin 𝐴sin 𝐵

sin ( 𝐴+𝐵 )=sin 𝐴 cos𝐵+cos 𝐴sin𝐵

cos ( 𝐴−𝐵 )=cos 𝐴 cos𝐵+sin 𝐴sin𝐵

tan ( 𝐴+𝐵 )= tan 𝐴+ tan 𝐵1− tan 𝐴 tan 𝐵

Trigonometry

Compound Angles

BASIC FORMULAE



𝑃=𝑎+𝑏+𝑐

𝐶=2𝜋 𝑟

𝑃=2𝑙+2𝑏 𝐴=𝑙𝑏

𝐴=𝜋 𝑟2

𝐴=12𝑏 h

Geometry

Perimeter AreaShape

a

b

ch

lb

r

BASIC FORMULAE



Author: M. D. Raghu

[email protected]

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