tan2x Formula
Tangent which is also known as the tan is one of the six trigonometric ratios. In a given right triangle, the tangent of an angle is calculated as the opposite side divided by the adjacent side of the given angle. Double angle formulas are the trigonometric functions that have double angles such as sin2x, cos2x, etc. Hence, tan2x is also a double angle function of a tangent. Let's look into the tan2x formula in detail.
Formula to Calculate tan2x
Tan2x Formula is also known as the double angle function of tangent.
Let's look into the double angle function of tangent i.e, tan2x Formula is as shown below.
tan 2x = 2tan x / 1−tan^{2}x
where,
 tan x = Opposite Side / Adjacent Side
 tan 2x = Double angle function of tan x
 tan^{2}x = Square funtion of tan x
i.e, tan^{2}x = (tan x)^{2}
Now, let's represent tan 2x formula in terms of sin and cos functions
We know that,
tan x = sin x / cos x
Thus,
tan 2x = sin 2x / cos 2x  (1)
sin 2x = 2 sin x cos x  (2)
cos 2x = cos^{2}x  sin^{2}x  (3)
Substituting the value of (2) and (3) in (1) we get,
tan 2x = 2 sin x cos x / cos^{2}x  sin^{2}x
Let's look into some examples using tan2x formula
Solved Examples using tan2x Formula

Example 1: Find tan 2x, if tan x = 7 using tan2x formula.
Solution:
According to tan 2x formula,
tan2x = 2tanx / 1−tan^{2}x
tan x = 7
tan^{2}x = 49
tan2x = (2×7) / (1−49)
= 14 / (48)
= 7 / 24
Answer: Thus, the value of tan 2x is 7 / 24.

Example 2: If sin x = 3/5 and cos x = 4/5, find the value of tan 2x.
Solution:
We know that according to tan 2x formula in terms of sin x and cos x is given by,
tan 2x = 2 sin x cos x / cos^{2}x  sin^{2}x
= [2 × (3/5) × (4/5)] / [ (16/25)  (9/25)]
= (24/25) / (7/25)
= 24/7
Answer: Thus, the value of tan 2x is 24/7.