Answer:
tan([tex]\frac{A}{2}[/tex] ) = ± [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Using the trigonometric identity
tan ([tex]\frac{A}{2}[/tex] ) = ± [tex]\sqrt{\frac{1-cosA}{1+cosA} }[/tex]
Given
tanA = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
This is a right triangle 5- 12- 13 ( with hypotenuse 13 ), then
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex] , then
tan ([tex]\frac{A}{2}[/tex] )
= ± [tex]\sqrt{\frac{1-\frac{12}{13} }{1+\frac{12}{13} } }[/tex]
= ± [tex]\sqrt{\frac{\frac{1}{13} }{\frac{25}{13} } }[/tex]
= ± [tex]\sqrt{\frac{1}{25} }[/tex]
= ± [tex]\frac{1}{5}[/tex]
