# Homework Help: Trigonometry and Identities

1. May 1, 2016

### Veronica_Oles

1. The problem statement, all variables and given/known data
sin^2x + 4sinx +4 / sinx + 2 = sinx +2

2. Relevant equations

3. The attempt at a solution
L.S = sin^2x + 4sinx +4 / sinx + 2
=1-cos^2+4(sinx + 1) / sinx +2

Not sure where to go from there.
Not sure if I was even supposed to factor out the 4?

2. May 1, 2016

### SammyS

Staff Emeritus
Please enclose the entirety of any numerator and/or denominator in parentheses.

3. May 1, 2016

### Veronica_Oles

(Sin^2x + 4sinx + 4) / (sinx + 2) = sinx + 2

4. May 1, 2016

### SammyS

Staff Emeritus
Factor the numerator.

5. May 1, 2016

### Veronica_Oles

Thank you, didn't catch that.

6. May 1, 2016

### SammyS

Staff Emeritus
So, what do you get ?

7. May 1, 2016

### Veronica_Oles

((Sinx + 2)(Sinx + 2)) / (Sinx + 2)

Then you cancel one from top and bottom to get: Sinx + 2.

8. May 1, 2016

### micromass

Yes, but it is a tiny bit more complicated. Here's something to think about:

1) Why doesn't the following equality hold for all $x$:

$$\frac{(x+2)(x+2)}{x+2} = x+2$$

2) Why is this no problem with the question in the OP?

9. May 1, 2016

### Veronica_Oles

((Sinx + 2)(Sinx + 2)) you then take reciprocal of denominator and multiply it by the numerator, and that it is when you cancel them out?

10. May 2, 2016

### Math_QED

Can you always divide out common factors from numerator and denumerator? For example, can you always say that (cosx-1)(cosx + 1)/(cosx - 1) = cosx + 1?

Why can/can't you say that? And what about your expression, those are things you have to think about!

11. May 3, 2016

### zr95

To give you a hint, what happens if we plug in -2 for x? Pay attention to the denominator.

12. May 3, 2016

### Staff: Mentor

micromass asked two questions. You didn't respond to his first question, and your answer to the second question doesn't address why $\frac{(\sin x+2)(\sin x+2)}{\sin x+2} = \sin x+2$ is always true, regardless of the value of x.