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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 ORTHOCENTER AND PEDAL TRIANGLE OF A TRIANGLE. In a triangle the altitudes drawn from the three vertices to the opposite sides are concurrent and the point of cuncurrency of the altitudes of the triangle is called the orthocenter of the triangle. The triangle formed by joining the feet of these perpendiculars is called the pedal triangle i.e. DEF is the pedal triangle of ABC. 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 Inscribed & Circumscribed Polygons
(Important Formulae) 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.  ## Inverse-Trigonometric-Functions-objectives-with-solutions-Trigonometry-IIT JEE MATHS-Mains / Advanced

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

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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)

SOLUTION

## Properties-of-Triangle-objectives-with-solutions-Trigonometry-IIT JEE MATHS-Mains / Advanced

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

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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

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

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

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

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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

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

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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

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

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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

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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

SOLUTION

## Solution-of-Triangle-objectives-12-Trigonometry-IIT JEE MATHS-Mains / Advanced

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

PROBLEM

SOLUTION

## Solution-of-Triangle-objectives-11-Trigonometry-IIT JEE MATHS-Mains / Advanced

To understand this question of properties of triangles you must know;  The concept  of circum-centre and circum-radius and sine rule

PROBLEM