
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Tan2x Formula
Trigonometry is a mathematical area that uses trigonometric ratios to calculate the angles and unknown sides of a triangle. It facilitates the estimate of unknown dimensions of a rightangled triangle by employing equations and identities based on this relationship. Trigonometry is defined by the terms ‘Trigonon’ and ‘Metron,’ which symbolise a triangle and a measurement, respectively. This field of mathematics is investigated utilising trigonometric ratios such as sine, cosine, tangent, cotangent, secant, and cosecant. It is the investigation of the connection between the sides and angles of a rightangled triangle.
Quick Links
ToggleA trigonometric ratio is the ratio of the lengths of any two sides of a right triangle. These ratios link the sides of a right triangle to their angles in trigonometry. The tangent ratio is determined by dividing the length of an angle’s opposing side by the length of its neighbouring side. It is abbreviated as tan.
What is Tan2x in Trigonometry?
Tan2x is a trigonometric function with a formula that can be used to solve different trigonometric issues. The Tan2x Formula is a useful doubleangle formula or a trigonometry formula in which the angle is doubled. It can be stated in terms of tan x as well as a sin2x/cos2x ratio. Because the reciprocal of tan x is cot x, students can write tan2x as the reciprocal of cot 2x, i.e. tan2x = 1/cot2x.
Tan2x Formula
The Tan2x Formula is a doubleangle identity in trigonometry. The tangent function can alternatively be written as tan2x = sin 2x/cos 2x since it is a ratio of the sine and cosine functions. The Tan2x Formula is a crucial trigonometric identity that is used to solve a variety of trigonometric and integration issues. The value of tan2x repeats every 2π radians, tan2x = tan (2x + 2π). The Tan2x Formula has a considerably smaller graph than tan x. It is a trigonometric function that returns the tan function value of a double angle.
The Tan2x Formula can be expressed in two ways. It can be represented solely in terms of the tangent function or as a mix of the sine and cosine functions.
The Tan2x Formula identity is given as:
The Tan2x Formula = 2tan x / (1−tan2x)
The Tan2x Formula = sin 2x/cos 2x
Tan2x Formula Proof
The Tan2x formula can be obtained in two ways. First, students will obtain the tan2x identity using the angle addition formula for the tangent function. It is worth noting that the double angle 2x can be written as 2x = x + x. To prove the formula for tan2x, students will utilise the trigonometric formula:
tan (a + b) = (tan a + tan b)/(1 – tan a tan b)
they have
The Tan2x Formula = tan (x + x)
= (tan x + tan x)/(1 – tan x tan x)
= 2 tan x/(1 – tan2x)
As a result, they used the angle sum formula of the tangent function to obtain the Tan2x Formula.
Tan2x Identity Proof Using Sin and Cos
A trigonometric ratio is the length ratio of any two sides of a right triangle. These ratios connect the ratio of sides of a right triangle to trigonometric angles. The tangent ratio is determined by dividing the length of an angle’s opposing side by the length of its neighbouring side. Tan is the acronym for it.
 tan x = sin x/ cos x
 sin 2x = 2 sin x cos x
 cos 2x = cos^{2}x – sin^{2}x
Using the above formulas, we have
tan2x = sin 2x/cos 2x
= 2 sin x cos x/(cos^{2}x – sin^{2}x)
Divide the denominator and numerator of 2 sin x cos x/(1 – 2 sin^{2}x) by cos^{2}x
tan2x = [2 sin x cos x/cos^{2}x]/[(cos^{2}x – sin^{2}x)/cos^{2}x]
= (2 sin x/cos x)/(1 – sin^{2}x/cos^{2}x)
= 2 tan x/(1 – tan^{2}x)
Tan2x Graph
The graph of tan2x resembles the graph of tan x. Students already know what the period of tan x is.π Because π/b gives the period of tan bx, the period of tan2x is π/2. The graph of tan2x is shown below, and as can be seen, the value of tan2x repeats every π/2 radian. Also, because tanx is equal to zero anytime x is an integral multiple of π, tan2x is equal to zero whenever 2x = nπ, where n is an integer, implying that the graph below has xintercepts at x = nπ/2.
Tan^2x (Tan Square x)
Tan^2x is the trigonometric function tanx squared. Using trigonometric identities and formulae including tan^2x, one can get the tan square x formulas. Because tan x can be represented as a ratio of sinx and cosx, they can define tan2x as a ratio of sin square x and cos square x. The tan^2x formula is used to handle difficult integration and differentiation issues as well as to simplify trigonometric formulas. The formula for tan square x will be deduced and discussed in the next section.
Tan^2x Formula
Students now have a trigonometric identity 1 + tan^2x = sec^2x, implying tan^2x = sec^2x – 1. Because tan x can be defined as the ratio of the sine function and the cosine function, they can write tans square x as the ratio of sin square x and cos square x, yielding tan^2x = sin^2x / cos^2x. Also, because tan x is the reciprocal of cot x, they can write tan^2x = 1/cot^2x. As a result, the following tan^2x formulas are listed:
tan^2x = sec^2x – 1 ⇒ tan2x = sec2x – 1
tan^2x = sin^2x / cos^2x ⇒ tan2x = sin2x/cos2x
tan^2x = 1/cot^2x ⇒ tan2x = 1/cot2x
Tan2x in Terms of Cos
In terms of cos, one can get the Tan2x Formula. To express tan2x in terms of cos x, they shall utilise the trigonometric formulae shown below.
tan x = sin x/ cos x
sin 2x = 2 sin x cos x
cos 2x = 2 cos2x – 1
sin x = √(1 – cos2x)
Student will have after using the above formulas,
The Tan2x Formula = sin 2x/ cos 2x
= 2 sin x cos x/(2 cos2x – 1)
= [2 √(1 – cos2x) cos x/(2 cos2x – 1)]
Similarly, they can write tan2x in terms of sin using the trigonometric identities.
The Tan2x Formula = [2 sin x/(1 – 2 sin2x)]√(1 – sin2x)
Solved Examples
If tan x = 4/5, calculate the value of tan 2x.
Solution: We have, tan x = 4/5.
Using the formula we get,
tan 2x = 2 tan x/(1 – tan^{2} x)
= (2 (4/5))/(1 – (4/5)^{2})
= (8/5)/(1 – 16/25)
= (8/5)/(9/25)
= 72/125
FAQs (Frequently Asked Questions)
1. What is the Tan2x Formula in trigonometry?
The Tan2x Formula is a fairly popular doubleangle trigonometric formula that can be stated in terms of several trigonometric functions such as tan x, cos x, and sin x. Tan2x is generally defined as
The Tan2x Formula = 2tan x / (1 tan2x).
2. What Is the Distinction Between Tan^^2x and Tan2x?
The Tan2x Formula is a trigonometric doubleangle formula that calculates the tangent function for the compound angle 2x. Tan^2x, on the other hand, is the whole square of the trigonometric function tanx. The Tan2x Formula can have both positive and negative values, whereas tan2^x is always nonnegative, since the square of an integer is never negative.
3. What is a Tan Function?
Normally, the Tangent Angle Formula is used to compute the angle of a rightangle triangle. The tangent of an angle in any given right triangle is the length of the opposing side divided by the length of the neigh bouring side. The tangent function is one of the three most popular trigonometric functions, along with sine and cosine. The tangent of an angle in any given right angle is the length of the opposing side divided by the length of the neigh bouring side.
Students can just write it as ‘tan’ in a formula.
The tan formula is calculated by dividing opposed sides by adjacent sides.
Trigonometric formulae such as Sin 2x, Cos 2x, and Tan 2x are known as doubleangle formulas because their trigonometric functions include double angles.
There are two ways to represent the tan 2x expression. This can only be written as a tangent function and as a sine and cosine function combination. The formula for the tan 2x identity is as follows:
Tan 2x equals sin 2x/cos 2x