Answer:
-8/15
Explanations:
Given the following parameters
tan(x) = 4
sin(x) is positive
Required
tan(2x)
According to the double angle formula
[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}[/tex]
Applying this formula to expand tan(2x)
[tex]\begin{gathered} \tan (2x)=\tan (x+x)=\frac{\text{tanx}+\tan x}{1-\text{tanxtanx}} \\ \tan (2x)=\frac{2\tan x}{1-\tan^2x} \end{gathered}[/tex]
Substitute tan(x) = 4 into the expression:
[tex]\begin{gathered} \tan (2x)=\frac{2\tan x}{1-\tan^2x} \\ \tan (2x)=\frac{2(4)}{1-4^2} \\ \tan (2x)=\frac{8}{1-16} \\ \tan (2x)=-\frac{8}{15} \end{gathered}[/tex]
Hence the value of tan(2x) is given as -8/15
