Question

Use the following information to determine tan(2x).tan(x) = 4 and sin(x) is positive

Answer 1

-8/15

Explanations:

Given the following parameters

tan(x) = 4

sin(x) is positive

Required

tan(2x)

According to the double angle formula

`\tan (A+B)=(\tan A+\tan B)/(1-\tan A\tan B)`

Applying this formula to expand tan(2x)

`\begin{gathered} \tan (2x)=\tan (x+x)=\frac{\text{tanx}+\tan x}{1-\text{tanxtanx}} \\ \tan (2x)=(2\tan x)/(1-\tan^2x) \end{gathered}`

Substitute tan(x) = 4 into the expression:

`\begin{gathered} \tan (2x)=(2\tan x)/(1-\tan^2x) \\ \tan (2x)=(2(4))/(1-4^2) \\ \tan (2x)=(8)/(1-16) \\ \tan (2x)=-(8)/(15) \end{gathered}`

Hence the value of tan(2x) is given as -8/15