Answer:
[tex]\frac{1}{7}[/tex]
Step-by-step explanation:
Given
tanx = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
This is a 3- 4- 5 right triangle with hypotenuse = 5, then
cosx = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex]
Then
[tex]\frac{cosx-sinx}{cosx+sinx}[/tex]
= [tex]\frac{\frac{4}{5}-\frac{3}{5} }{\frac{4}{5}+\frac{3}{5} }[/tex]
= [tex]\frac{\frac{1}{5} }{\frac{7}{5} }[/tex]
= [tex]\frac{1}{5}[/tex] × [tex]\frac{5}{7}[/tex]
= [tex]\frac{1}{7}[/tex]
