Trigonometric identities are equalities where we would have trigonometric functions and they would be true for every value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles.


sinθ = Opposite side/Hypotenuse side

cosθ = Adjacent side/Hypotenuse side

tanθ = Opposite side/Adjacent side

cscθ = Hypotenuse side/Opposite side

secθ = Hypotenuse side/Adjacent side

cotθ = Adjacent side/Opposite side

Reciprocal Trigonometric Identities 

sinθ = 1/cscθ

cscθ = 1/sinθ

cosθ = 1/secθ

secθ = 1/cosθ

tanθ = 1/cotθ

cotθ = 1/tanθ

Other Trigonometric Identities

sin2θ  + cos2θ = 1

sin2θ = 1 - cos2θ

cos2θ = 1 - sin2θ

sec2θ - tan2θ = 1

sec2θ = 1 + tan2θ

tan2θ = sec2θ - 1

csc2θ - cot2θ = 1

csc2θ = 1 + cot2θ

cot2θ = csc2θ - 1

Compound Angles Identities

sin(A + B) = sinAcosB + cosAsinB

sin(A + B) = sinAcosB + cosAsinB

cos(A + B) = cosAcosB - sinAsinB

cos(A - B) = cosAcosB + sinAsinB

tan(A + B) =  (tanA + tanB)/(1 - tanAtanB)

tan(A - B) =  (tanA - tanB)/(1 + tanAtanB)

Double Angle Identities

sin2A = 2sinAcosA

cos2A = cos2A - sin2A

tan2A =  2tanA/(1 - tan2A)

cos2A = 1 - 2sin2A

cos2A = 2cos2A - 1

sin2A = 2tanA/(1 + tan2A)

cos2A = (1 - tan2A)/(1 + tan2A)

sin2A = (1 - cos2A)/2

cos2A = (1 + cos2A)/2

Half Angle Identities

sinA = 2sin(A/2)cos(A/2)

cosA = cos2(A/2) - sin)2(A/2)

tanA = 2tan(A/2)/[1 - tan2(A/2)]

cosA = 1 - 2sin2(A/2)

cosA = 2cos2(A/2) - 1

sinA = 2tan(A/2)/[1 + tan2(A/2)]

ccosA = [1 - tan2(A/2)]/[1 + tan2(A/2)]

sin2(A/2) = (1 - cosA)/2

ccos2(A/2) = (1 + cosA)/2

tan2(A/2) = (1 - cosA)/(1 + cosA)

Triple Angle Identities

sin3A = 3sinA - 4sin3A

cos3A = 4cos3A - 3cosA

tan3A = (3tanA - tan3A)/(1 - 3tan2A)

Sum to Product Identities

sinC + sinD  =  2sin[(C + D)/2]2cos[(C - D)/2]

sinC - sinD = 2cos[(C + D)/2]sin[(C - D)/2]

cosC + cosD = 2cos[(C + D)/2]cos[(C - D)/2]

cosC - cosD = 2sin[(C + D)/2] ⋅ sin[(C - D)/2]

Values of Trigonometric Ratios for Standard Angles

Solving Word Problems Using Trigonometric Identities

Step 1 :

Understanding the question and drawing the appropriate diagram are the two most important things to be done in solving word problems in trigonometry.

Step 2 :

If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.

Step 3 :

We have to draw diagram almost for all of the word problems in trigonometry. The diagram we draw for the given information must be correct. Drawing diagram for the given information will give us a clear understanding about the question. 

Step 4 :

Once we understand the given information clearly and correct diagram is drawn, solving word problems in trigonometry would not be a challenging work. 

Step 5 :

After having drawn the appropriate diagram based on the given information, we have to give name for each position of the diagram using English alphabets (it is clearly shown in the word problem given below). Giving name for the positions would be easier for us to identify the parts  of the diagram.

Step 6 :

Now we have to use one of the three trigonometric ratios (sin, cos and tan) to find the unknown side or angle.

Once the diagram is drawn and we have translated the English Statement (information) given in the question as mathematical equation using trigonometric ratios correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown. 

These are the most commonly steps involved in solving word problems in trigonometry.

Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to

We always appreciate your feedback.


Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power


Quantitative aptitude

Multiplication tricks


Aptitude test online


Test - I

Test - II


Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices





Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet


SAT - Math Practice

SAT - Math Worksheets

Hardest SAT Math Questions with Answers

Hardest PSAT Math Questions with Answers



Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem


Mensuration formulas

Area and perimeter



Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry questions 

Angle bisector theorem

Basic proportionality theorem


Coordinate geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance


Area of triangle

Area of quadrilateral


Matrix Calculators

Coordinate geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator


Missing addend 

Double facts 

Doubles word problems


Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work


Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry


Converting metric units

Converting customary units


HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and Venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree


Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

©All rights reserved.

Recent Articles

  1. Linear vs Exponential Growth

    May 23, 22 01:59 AM

    Linear vs Exponential Growth - Concept - Examples

    Read More

  2. Exponential vs Linear Growth Worksheet

    May 23, 22 01:42 AM

    Exponential vs Linear Growth Worksheet

    Read More

  3. SAT Math Questions on Exponential vs Linear Growth

    May 23, 22 01:34 AM

    SAT Math Questions on Exponential vs Linear Growth

    Read More