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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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Arithmetic
𝒕𝒏=𝒂𝒓𝒏−𝟏
𝒓=𝒕𝒏𝒕𝒏−𝟏
Arithmetic Series
𝑎 ,𝑎+𝑑 ,𝑎+2𝑑 ,…Geometric Series
𝑎 ,𝑎𝑟 ,𝑎𝑟2 ,…
BASIC FORMULAE
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Coordinates and Gradients
BASIC FORMULAE
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Analytical Geomtery
Line Equations
BASIC FORMULAE
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
𝒔𝒊𝒏𝜽=𝒚𝒓
𝒄𝒐𝒔 𝜽=𝒙𝒓
𝒕𝒂𝒏𝜽=𝒚𝒙
𝒄𝒐𝒔𝒆𝒄 𝜽=𝒓𝒚
𝒔𝒆𝒄 𝜽=𝒓𝒙
𝒄𝒐𝒕 𝜽=𝒙𝒚
Trigonometry
Ratios
x
yr
θ
BASIC FORMULAE
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
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
FOR STUDENTSMATHEMATICS
©2014 MDR www.learningforknowledge.com/glg
Author: M. D. Raghu
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