The value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
tanx = 3/4 (x is an acute angle)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}-1=\dfrac{4}{3}-1\\\\\rm \dfrac{cosx-sinx}{sinx}=\dfrac{1}{3}\\\\[/tex] ….(1)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}+1=\dfrac{4}{3}+1\\\\\rm \dfrac{cosx+sinx}{sinx}=\dfrac{7}{3}\\\\[/tex] …(2)
Divide (1) ÷ (2)
(cosx-sinx)/(cosx+sinx) = (1/3)/(7/3) = 1/7
Thus, the value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
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