INTEGRATION SHORT TRICK

TRIGONOMETRY Nth DERIVATIVE SHORT TRICK

#PERMUTATION AND COMBINATION# SUPER SHORT TRICK#IITJ-EE/GRE/GMAT/SSC -C...

#SHORT TRICK# HOW TO FIND RANK OF WORD IN DICTIONARY WITH REPETITION #

#SHORT TRICK#HOW TO FIND RANK OF WORD IN DICTIONARY #

SHORT TRICK FOR INTEGRATION BY PARTS

LIMIT TRICK //SHORTCUT//IITJEE//NDA//CET//AIRFORCE//BITSAT//RAILWAYS

#DIFFERENTIATION SHORT CUT #DERIVATIVE TRICKS //SOLUTION IN 3 SECONDS

HIGHER ORDER DERIVATIVE SHORT TRICK (nth derivative )

#SHORT TRICK # TERM INDEPENDENT OF X#

#COMPLEX NUMBER# SHORT TRICK#

LIMIT SHORT CUT SOLVE IN 2 SECONDS

#COMPLEX NUMBER #SHORT TRICK #LOCUS OF A POINT #

#SHORT TRICK FOR POINT OF INTERSECTION OF STRAIGHT LINES #

#SHORT TRICK ON STRAIGHT LINES # COORDINATE GEOMETRY

Short Trick for Differentiation of Series functions

DIFFERENTIATION SHORT TRICK FOR TYPE F(X) POWER G(X) FUNCTIONS

SHORT TRICK FOR DIFFERENTIATION OF IMPLICIT FUNCTIONS

#TRIGONOMETRIC SHORT TRICK #

#SEQUENCE AND SERIES SHORT TRICK #AP#JEE

#INTEGRATION SUPER SHORT CUT #JEE

#TRIGONOMETRY SHORT CUT #JEE

#Differential Equations #SHORT TRICK#JEE

DEFINITE INTEGRATION SHORT TRICK#JEE

INTEGRATION SUPER SHORT TRICK#JEE

AM/GM/HM SUPER SHORT TRICK#JEE

Limit Super Short Trick #JEE

Super Short Trick for parabola. Important for IIT JEE

Super Short Trick to find inverse of function. Important for IIT JEE

#LDE of second order # method of variations of parameter

#LDE of Second Order # Solutions by means of operational factors

#LDE 2nd Order # Removal of first Derivative # Normal form

Jacobians

domain of functions

domain and range of functions by graphs

variables in functions

Properties of Addition of Vectors

Rectangular Resoultion of Vector and Direction Cosines

Basic Concept of Vectors

maxima and minima of two variables

Lagrange method of undetermined multiplier

Green Theorem

Gauss or Divergence Theorem

Stokes Theorm

HOMOGENEOUS FUNCTIONS AND EULER THEOREM

Line Integral

Simultaneous Differential Equations

Iteration Method

Bayes Theorem and Total Probability . Important for IIT JEE AND GATE

Newton Raphson Method

False Position Method

Gradient of Vector Function

Divergence and Curl of Vector Function

Taylor Series Method Explained with Example

Taylor Series Method Explained with Example

Iteration Method explained with an example

Short Trick for eigen values of Matrices ? ( in Hindi ) . Important f...

Properties of Eigen Values of Matrices . Important for GATE exam

Rank of 4 x 4 order Matrices ??? Three Step Only ?( in Hindi ) . Impor...

Find Rank of 3 x 4 order Matrices ??? Two step Method ? ( in Hindi ) . I...

Rank of 3 x 3 order Matrices ??? ( in Hindi ) . Important for GATE Stud...

Short trick to find inverse of matric

https://youtu.be/dRm3bsY9EZs

Important Short Tricks on Trigonometric indenties

Important Short Tricks on Trigonometric.  Indenties

Pythagorean Identities

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

cot² θ + 1 = csc² θ

Negative of a Function

sin (–x) = –sin x

cos (–x) = cos x

tan (–x) = –tan x

csc (–x) = –csc x

sec (–x) = sec x

cot (–x) = –cot x

If A + B = 90^o, Then

Sin A = Cos B

Sin²A + Sin²B = Cos²A + Cos²B = 1

Tan A = Cot B

Sec A = Csc B

For example:    

If tan (x+y) tan (x-y) = 1, then find tan (2x/3)?

Solution:            

Tan A = Cot B, Tan A*Tan B = 1

So, A +B = 90^o

(x+y)+(x-y) = 90^o, 2x = 90^o , x = 45^o

Tan (2x/3) = tan 30^o = 1/√3

If A - B = 90^o, (A › B) Then

Sin A = Cos B

Cos A = - Sin B

Tan A = - Cot B

If A ± B = 180^o, then

Sin A = Sin B

Cos A = - Cos B

If A + B = 180^o                   

Then, tan A = - tan B

If A - B = 180^o                    

Then, tan A = tan B

 

If A + B + C = 180^o, then

Tan A + Tan B +Tan C = Tan A * Tan B *Tan C

sin θ * sin 2θ * sin 4θ = ¼ sin 3θ

cos θ * cos 2θ * cos 4θ = ¼ cos 3θ

For Example:What is the value of cos 20^ocos 40^o cos 60^o cos 80^o?

Solution: We know cos θ * cos 2θ * cos 4θ = ¼ cos 3θ

Now, (cos 20^o cos 40^o cos 80^o ) cos 60^o

¼ (Cos 3*20) * cos 60^o

¼ Cos² 60^o = ¼ * (½)² = 1/16

If             a sin θ + b cos θ = m     &    a cos θ - b sin θ = n

then a² + b² = m² + n²

For Example:

If 4 sin θ + 3 cos θ = 2 , then find the value of  4 cos θ - 3 sin θ:

Solution:

Let 2 cos θ - 3 sin θ = x

By using formulae a² + b² = m² + n²

4² + 3² = 2² + x²

16 + 9 = 4 + x²

X = √21

If

sin θ +  cos θ = p     &     csc θ -  sec θ = q

then P – (1/p) = 2/q

For Example:

If sin θ + cos θ = 2 , then find the value of  csc θ - sec θ:

Solution:

By using formulae:

P – (1/p) = 2/q

2-(1/2) = 3/2 = 2/q

Q = 4/3 or csc θ - sec θ = 4/3

If

a cot θ + b csc θ = m     &    a csc θ + b cot θ = n

then b² - a²  = m² - n²

If

cot θ + cos θ = x     &    cot θ - cos θ = y

then x² - y² = 4 √xy

If

tan θ + sin θ = x     &    tan θ - sin θ = y

then x² - y² = 4 √xy

If

y = a² sin²x + b² csc²x + c

y = a² cos²x + b² sec²x + c

y = a² tan²x + b² cot²x + c

then,

y_min = 2ab + c

y_max = not defined

For Example:                    

If y = 9 sin² x + 16 csc² x +4 then y_min is:

Solution:            

For, y min = 2* √9 * √16 + 4

= 2*3*4 + 20 = 24 + 4 = 28

If            

y = a sin x + b cos x + c

y = a tan x + b cot x + c

y = a sec x + b csc x + c

then,     y_min = + [√(a²+b²)] + c

y_max = - [√(a²+b²)] + c

For Example:                    

If y = 1/(12sin x + 5 cos x +20) then y_maxis:

Solution:            

For, y max = 1/x min

= 1/- (√12² +5²) +20 = 1/(-13+20) = 1/7

Sin² θ, maxima value = 1, minima value = 0

Cos² θ, maxima value = 1, minima value = 0