tan¦È=7/24 then prove that

¡Ì(1-cos¦È/1+cos¦È)=1/7
WHERE 0<¦È<90¡ã

using more conventional symbols, I assume we have

tanθ = 7/24, in the 1st quadrant.
So, cosθ = 24/25

I expect you can do the arithmetic now, eh?