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

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