Question 734052
if cotx + cosecx = 1.5, then prove that cosx = 5/13
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
cosx=5/13=A/H
A=5, H=13
{{{O=sqrt(H^2-A^2)=sqrt(13^2-5^2)=sqrt(169-25)=sqrt(144)=12}}}
{{{cotx=A/O=5/12}}}
{{{cscx=H/O=13/12}}}
{{{cotx+cscx=18/12=1.5}}}
This proves that if cotx+cscx=1.5, cosx = 5/13, because both equations come from the same 5-12-13 right triangle