We know that the derivative of trigonometric function tan x is given by sec 2x. Hence we have derived the tan 2x formula by expressing it as a ratio of sin 2x and cos 2x. We will use the following trigonometric formulas:ĭivide the numerator and denominator of 2 sin x cos x/(1 - 2 sin 2x) by cos 2x Now, we will derive the tan 2x formula by expressing tan as a ratio of sin and cos. Hence, we have derived the tan 2x formula using the angle sum formula of the tangent function. tan (a + b) = (tan a + tan b)/(1 - tan a tan b).We will use the following trigonometric formula to prove the formula for tan 2x: Note that we can write the double angle 2x as 2x = x + x. First, we will use the angle addition formula for the tangent function to derive the tan 2x identity. Tan 2x formula can be derived using two different methods.
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