sin 2A in Terms of tan A

We will learn how to express the multiple angle of sin 2A in terms of tan A.

Trigonometric function of sin 2A in terms of tan A is also known as one of the double angle formula.

We know if A is a number or angle then we have,

sin 2A = 2 sin A cos A

⇒ sin 2A = 2  \(\frac{sin A}{cos A}\) ∙ cos\(^{2}\) A

⇒ sin 2A = 2 tan A ∙  \(\frac{1}{sec^{2} A}\)

⇒ sin 2A = \(\frac{2  tan A}{1 + tan^{2} A}\)

There for sin 2A =  \(\frac{2  tan A}{1 + tan^{2} A}\)

Now, we will apply the formula of multiple angle of sin 2A in terms of tan A to solve the below problem.

1. If sin 2A = 4/5 find the value of tan A (0 ≤ A ≤ π / 4)

Solution:

Given, sin 2A = 4/5  

Therefore, \(\frac{2  tan A}{1  +  tan^{2} A}\) = 4/5

 ⇒ 4 + 4 tan\(^{2}\) A = 10 tan A            

⇒ 4 tan\(^{2}\) A - 10 tan A + 4 = 0

⇒ 2 tan\(^{2}\) A - 5 tan A + 2 = 0

⇒ 2 tan\(^{2}\) A - 4 tan A - tan A + 2 = 0

⇒ 2 tan A (tan A - 2) - 1 (tan A - 2) =0

⇒ (tan A - 2) (2 tan A - 1) = 0

Therefore, tan A - 2 = 0 and 2 tan A - 1 = 0

⇒ tan A = 2 and tan A = 1/2

According to the problem, 0 ≤ A ≤ π/4     

Therefore, tan A = 2 is impossible

Therefore, the required value of tan A is 1/2.

 Multiple Angles






11 and 12 Grade Math

From sin 2A 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. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More