# An elusive trig proof I can't seem to get

## Homework Statement

Prove that:

(sin(x)+ tan(x))/(cos(x)+ 1)= tan(x)

## Homework Equations

There are just trig identities that we can use.

## The Attempt at a Solution

I've attempted every possible way I can think of and it would just look like jibberish here.

Last edited:

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
What you wrote, sin(x)+ tan(x)/cos(x)+ 1= tan(x). isn't true! For example, if x= 0, then sin(x)= sin(0)= 0, tan(x)/cos(x)= tan(0)/cos(0)= 0/1= 0 so the left side is 1. But the right side, tan(x)= tan(0), is 0.

What I think you meant was (sin(x)+ tan(x))/(cos(x)+ 1)= tan(x).

If you multiply both sides of the equation by cos(x) you get
(sin(x)cos(x)+ sin(x))/(cos(x)+ 1)= sin(x).

Sorry yeah, that's what I meant, my mistake. I'll change that right now.

Use the fact that tan(x)=sin(x)/cos(x). The proof should just involve two lines of algebra.

factor out tan(x) from numerator and u get cos(x)+1 which cancels with denominator