Tan 2x Formula

Tan 2x Formula:

Tan 2x is a double-angle trigonometric function that can be represented as tan x, sin x, and cos x. The tan angle formula is used to calculate the angle of a right triangle. It has been found that the tangent to the angle of a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. 

It can be expressed as tan 2x or as a ratio of sin 2x to cos 2x. Since the reciprocal of tan x is cot x, we can write tan 2x as the reciprocal of cot 2x, that is,

 tan 2x= 1 / cot 2x .

What is a Tan Function?

The Tangent Angle Formula is normally used to calculate the angle of the right-angle triangle. In any given right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. 

The tangent function, along with sine and cosine, is known to be one of the three most common trigonometric functions. In any given right angle, the tangent of an angle is the length of the opposite side  divided by the length of the adjacent side .

In a formula, we can simply write it as ‘tan’.

The tan formula is given by the division of opposite sides by adjacent sides.

Trigonometric Formulas like Sin 2x, Cos 2x and Tan 2x are known as double angle formulas because these formulas have double angles in their trigonometric functions.

The tan 2x expression can be expressed in two different formats. This can only be expressed as a tangent function and as a combination of sine and cosine functions. The formula for the tan 2x identity is: 

Tan 2x=sin 2x/ cos 2x    

Let’s know how to derive the double angle tan 2x formula.

Tan 2x Formula Derivation 

Tan 2x expressions can be derived by using two different methods. First, we derive tan 2x identity using the angle addition formula of the tangent function. Note that you can write a double angle 2x as 2x=x+x. Prove the expression for tan 2x using the following trigonometric expression. 

Tan a+b=(tan a+tan b)/(1-tan a tan b )    

tan 2x=tan x+x= 2tan x/(1-tan x tan x)    

tan2x=2tanx/(1-tan² x)

Therefore, we have derived the tan 2x formula using the angle sum formula of the tangent function.