Help with trigonometric identites?

Question

Hi, can u help me with the following question please?

verify this identity: (sin x)/(sin x + cos x) = (tan x)/(1 + tan x).

How do i proof this?? im been stuck on this question like for hours!!! Please help me and show me step by step on how it is done.

Thank you!!

Answer 1

sinx / (sinx + cosx)

Divided by cosx numerator and denominator

= (sinx / cosx ) / ((sinx + cosx) / cosx)

= (sinx / cosx ) / ((sinx / cosx + cosx / cosx)

Recall : Trigonometry identity tanx = sinx / cosx

= tanx / tanx + 1 = (tanx) / (1 + tanx)

The trigonometry identity is proved.