Category: Trigonometry / IIT JEE MAINS/ADVANCED-FREE STUDY MATERIAL

It contains CONCEPTS AND SOLVED PROBLEMS Trigonometric ratios,Trigonometric equations,Trigonometric conditional identities,Trigonometric series,Properties of triangle,Inverse trignometry

Trigonometric conditional identities

1 Trigonometric ratios / Identities

Definition of Trigonometric Ratios,Fundamental Relations Between the trigonometrical Ratios of an Angle, Signs of Trigonometric Ratios ,Periods of Trigonometrical Functions,Graphs of The Trigonometric Ratios,Trigonometric Ratio for an Angle of any Magnitude,Trigonometric Ratios of Compound Angles,Trigonometric Ratios of Multiples of an Angle,Product of Sines/Cosines in terms of Sums & Vice-Versa ,Maximum and Minimum Values of a cos + b sin, Trigonometric Ratio of Submultiple of an Angle ,Identities

2 Trigonometric equations/Inequalities

Trigonometric Equation,Solution of a Trigonometric Equation,General Solution,Types of Trigonometric Equations,Some Important Points, Solving Simultaneous Equations Trigonometric In equations, Problem Based on Boundary Conditions

3 Trigonometric conditional
identities/ Trigonometric series

5 Properties of triangle :- Elements of a triangle,Sine Rule,Cosine Rule, Projection Formulae,Napier’s Analogy, Half-angle Formulae,Area of Triangle,m-n Thoerem,Centroid and Medians of a triangle,Circumcircle Orthocentre and Pedal triangle,of a triangle,Bisectors of the angles ,Incircle, Distance between the special points, Escribed circles,Excentral triangles,Solution of Triangles,Inscribed & Circumscribed Polygons

Video lectures of KAMAL SIR forProperties of triangles

QUICK REVIEW

In a triangle ABC the angles are denoted by capital letters A, B and C and the length of the sides opposite to these angles are denoted by small letters a, b and c. Semi perimeter of the triangle is
given by s where 2s = a + b+c and its area is denoted by Δ

SINE RULE

Sine rule is an important tool that relates side lengths with angles of triangles and circum radius of triangle

NAPIER’S ANALOGY (TANGENT RULE)

COSINE RULE
In a triangle ABC

PROJECTION RULE

(i) a = b cos C + c cos B (ii) b = c cos A + a cos C (iii) c = a cos B + b cos C

HALF ANGLE FORMULAE

.m-n THEOREM

CENTROID AND MEDIANS OF A TRIANGLE
The line joining any vertex of a triangle to the mid point of the opposite side of the triangle is called the median of the triangle. The three medians of a triangle are concurrent and the point of concurrency of the medians of any triangle is called the centroid of the triangle. The centroid divides the median
in the ratio 2 : 1.

Circum circle

The circle which passes through the angular points of a ABC, is called its circumcircle. The centre of this circle i.e., the point of concurrency of the perpendicular bisectors of the sides of the ABC, is called the circumcenter.

Radius of the circumcircle is given by the following formulae

BISECTORS OF THE ANGLES
If AD bisects the angle A and divide the base into portions x and y, we have, by Geometry,

INCIRCLE
the circle which can be inscribed within the triangle so as to touch each of the sides of the triangle is called its incircle. The centre of this circle i.e., the point of concurrency of angle bisectors of the triangle is called the incentre of the ABC

The distances Between the special points

ESCRIBED CIRCLES
The circle which touches the side BC and the two sides AB and AC produced is called the escribed circle opposite the angle A. Its centre and radius will be denoted by I1 and r1 respectively.

Excentral triangle
The triangle formed by joining the three excentres I1, I2 and I3 of
DABC is called the excentral or excentric triangle. Not that

SOLUTION OF TRIANGLES
When any three of the six elements (except all the three angles) of a triangle are given, the triangle is known completely. This process is called the solution of triangles.

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and simple trigonometric calculations

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and simple results involving inverse trigonometric calculations

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and result of tan(A+B)

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse

NOTE; Problem is not correct pz see the solution for correct problem

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and result of SIN(A+B)

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and how we get the range of simple quadratic functions

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their and domain and range of simple trigonometric functions

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and graphs of defining of arcSIN(sinx) and arcCOS(cosx)

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and defining of arcSIN(sinx) and solving simple quadratic inequalities

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and domain and range of inverse of trigonometric functions, solving simple quadratic inequalities

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and simple results involving inverse trigonometric functions ( arcTAN A -arcTAN B )

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and domain and range of simple inverse trigonometric functions

SOLUTION

PROBLEM

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and domain and range of inverse trigonometric functions

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse , domain and range of simple inverse trigonometric functions , concepts of quadratic equations

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse, domain and range and simple results

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse , how we change one inverse trigonometric function in 2 and result of ( arcTAN A -arcTAN B )

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse defining and graphs

SOLUTION

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse and result of sin (A- B)

To understand this question of properties of triangles you must know; The concept of sine rule

PROBLEM

SOLUTION

PROBLEM

To understand this question you must know; The concept of AM-HM inequality

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, and conditions when two circles touch each other

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of exradii, and conditions of AP,HP,GP

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule, basic concept of quadratic equation

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule, basic concept of quadratic equation

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of sine rule and triangle inequality

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of orthocentre , cicumcircle and circumradius

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule, sine rule and proving conditional trigo identities

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule, sine rule and proving conditional trigo identities

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of sine rule and ratio concept

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of solving trigo n quadratic inequalities

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule and conditions of cyclic quadrilateral

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius for regular polygon

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of inverse trigo functions and how we get sum of inverse trigonometric series

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of Cos rule

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of plane and line in vectors nd 3d

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept half angle results

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of half angle results, Tan or Naiper rule and area of triangle

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of angular bisector and sine rule

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of sine rule and conditions for existence of triangle

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius and conditions when two circles touch each other

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of circles and basic properties of circles

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept area and length of diagonal for square

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius ,excircle and exradii

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius and basic trigo inequalities

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of basic solving trigo equations and exponents

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of sine rule ,cos rule and simple trigo inequalities

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of solving simple trigo equations

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of incircle and in-radius, cicumcircle and circumradius

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of orthocente and lines of equations

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of sine rule and ex-centres and exradii

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know; The concept of cos rule