Answer:
tan2A = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Using the trigonometric identity
tan2A = [tex]\frac{2tanA}{1-tan^2A}[/tex], thus
tan2A = [tex]\frac{2(\frac{1}{5}) }{1-(\frac{1}{5})^2 }[/tex]
= [tex]\frac{\frac{2}{5} }{1-\frac{1}{25} }[/tex]
= [tex]\frac{\frac{2}{5} }{\frac{24}{25} }[/tex]
= [tex]\frac{2}{5}[/tex] × [tex]\frac{25}{24}[/tex] = [tex]\frac{5}{12}[/tex]
