Important Maths formula for CDSE

Below are some of the important formulas which will help you in CDSE, only a couple of topics have been covered in this post. Time limit in CDSE is less so the better you know the formulas the faster you will be able to solve your paper.


  1. log_b(x)=y \longleftrightarrow b^y=x
  2. log_b(xy)=log_bx+log_by
  3. log_b\frac{x}{y}=log_bx-log_by


Angle0\degree30 \degree45 \degree60 \degre90 \degree
TanA0\frac{1}{\sqrt{3}}1\sqrt{3}Not defined
CosecANot defined2\sqrt{2}\frac{2}{\sqrt{3}}1
SecA1\frac{2}{\sqrt{3}}\sqrt{2}2Not defined
CotANot defined\sqrt{3}1\frac{1}{\sqrt{3}}0
Trigonometric ratios asked in CDS examination.
  1. cos^2A +sin^2A=1
  2. 1+tan^1A=sec^2A for 0\degree \leq A \leq 90\degree
  3. cot^2A+1=cosec^2A for 0\degree < A \leq 90\degree
  4. cosecA=\dfrac{1}{sinA}
  5. secA=\dfrac{1}{cosA}
  6. tanA=\dfrac{sinA}{cosA}


  1. (x+y)^2=x^2+2xy+y^2
  2. (x-y)^2=x^2-2xy+y^2
  3. x^2-y^2=(x+y)(x-y)
  4. (x+a)(x+b)=x^2+(a+b)x+ab
  5. (x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx
  6. (x+y)^3=x^3+y^3+3xy(x+y)
  7. (x-y)^3=x^3-y^3+3xy(x-y)
  8. x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

Arithmetic Progression[AP]

  1. The general form of an AP is a, a + d, a + 2d, a + 3d, . . . . Where ‘d’ is called the common difference.
  2. If a,b, c are in AP, then b=\dfrac{a+c}{2}.
  3. In an AP with first term ‘a’ and common difference ‘d’, the nth term (or the general term) is given by a_n = a + (n -1) d.
  4. The sum(S) of the first n terms of an AP is given by, S=\dfrac{n}{2}[2a+(n-1)d].
  5. If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP is given by :S=\dfrac{n}{2}(a+l).

Quadratic equation

  1. A quadratic equation in the variable x is of the form ax^2 + bx + c = 0, where a, b, c are real numbers and a \neq 0.
  2. A real number \alpha is said to be a root of the quadratic equation ax^2 + bx + c = 0, if a \alpha^2 + b\alpha^2 + c = 0.
  3. Quadratic formula: The roots of a quadratic equation ax^2 + bx + c = 0 are given by \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}, provided b^2-4ac\geq0.
  4. A quadratic equation ax^2 + bx + c = 0 has,
    • Two distinct real roots if b^2-4ac > 0.
    • Two equal roots(i.e coincident roots) if b^2-4ac = 0.
    • No real roots if b^2-4ac < 0.

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