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




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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    Dec 15, 24 10:27 AM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  2. 2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line

    Dec 14, 24 02:12 PM

    Curved Line and Straight Line
    2nd grade geometry worksheet

    Read More

  3. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 14, 24 12:25 PM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  4. Patterns in Math | Missing Number | Counting Numbers | Worksheets

    Dec 13, 24 12:31 AM

    Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting

    Read More

  5. Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern

    Dec 12, 24 11:22 PM

    Patterns in Necklace
    Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si…

    Read More