tan A/2 in Terms of tan A

We will learn about the trigonometric ratios of tan A/3 in terms of angle tan A. 

How to find the value of tan A/2 in terms of tan A?

For all values of the angle A we know that, tan A = 2 tan A/2/1 - tan^2 A/2 

⇒ 2 tan A/2 = tan A ∙ tan^2 A/2

⇒ tan A ∙ tan^2 A/2 + 2 tan A/2 - tan A = 0 

⇒ tan θ/2 = -2 ± √(4 + 4 tan^2 A)/2 tan A

⇒ tan θ/2 = -1 ± √1 + tan^2A/tan A

How to determine the sign of tan A/2?

If A is given then we can easily find the quadrant in which A/2 lies.

Therefore, using the rule of “All, sin, tan, cos” we can find the exact signs of tan A/2. In other words, if the value of tan A is given then A can have infinite number of values.

Hence, it is not possible to find the exact quadrant in which A/2 will lie.

Therefore, we cannot find a definite value of tan A/2.  


 Submultiple Angles





11 and 12 Grade Math

From tan A/2 in Terms of tan A to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More