List of Maths Formulas for 12th Class

List of Maths Formulas for 12th Class

Here is a list of Maths formulas for CBSE class 12.

Vectors and Three Dimensional Geometry Formulas for Class 12

Position VectorOP=r⃗ =x2+y2+z2
Direction Ratiosl=ar,m=mr,n=cr
Vector AdditionPQ+QR=PR
Properties of Vector AdditionCommutativePropertya⃗ +b⃗ =b⃗ +a⃗ 
AssociativeProperty(a⃗ +b⃗ )c⃗ +=a⃗ +(b⃗ +c⃗ )
Vector Joining Two PointsP1P2=OP1OP1
Skew LinesCosθ=a1a2+b1b2+c1c2a21+a21+c21a22+a22+c22
Equation of a Linexx1a=yy1b=zz1c

Algebra Formulas For Class 12

Ifa⃗ =xi^+yj^+zk^ then magnitude or length or norm or absolute value of a⃗  is a=a=x2+y2+z2
A vector of unit magnitude is unit vector. If a⃗  is a vector then unit vector of a⃗  is denoted by a^ and a^=a^a^ Therefore a^=a^a^a^
Important unit vectors are i^,j^,k^, where i^=[1,0,0],j^=[0,1,0],k^=[0,0,1]
If l=cosα,m=cosβ,n=cosγ, then Î±,β,γ, are called directional angles of the vectorsa and cos2α+cos2β+cos2γ=1
In Vector Addition
a⃗ +b⃗ =b⃗ +a⃗ 
a⃗ +(b⃗ +c⃗ )=(a⃗ +b⃗ )+c⃗ 
k(a⃗ +b⃗ )=ka⃗ +kb⃗ 
a⃗ +0⃗ =0⃗ +a⃗ , therefore 0⃗  is the additive identity in vector addition.
a⃗ +(a⃗ )=a⃗ +a⃗ =0⃗ , therefore a⃗   is the inverse in vector addition.

Trigonometry Class 12 Formulas

Definition
θ=sin1(x)isequivalenttox=sinθ
θ=cos1(x)isequivalenttox=cosθ
θ=tan1(x)isequivalenttox=tanθ
Inverse Properties
sin(sin1(x))=x
cos(cos1(x))=x
tan(tan1(x))=x
sin1(sin(θ))=θ
cos1(cos(θ))=θ
tan1(tan(θ))=θ
Double Angle and Half Angle Formulas
sin(2x)=2sinxcosx
cos(2x)=cos2xsin2x
tan(2x)=2tanx1tan2x
sinx2=±1cosx2
cosx2=±1+cosx2
tanx2=1cosxsinx=sinx1cosx

Comments

Popular posts from this blog

Physics