1. ## Simpifying trigonometric expression

Hi,

I hope someone can help. I'm trying to simplify the following expression:

Apparently the answer is -√3x which is nowhere close to where my steps are going above. I'm curious where I am wrong in my steps?

Sincerely,
Olivia

2. ## Re: Simpifying trigonometric expression

Your sum of angles formula for $\sin(\alpha + \beta)$ is wrong.

3. ## Re: Simpifying trigonometric expression

Ok I got the right answer after I corrected the formula. Thanks for your help.

I have one last question. And it is regarding the last two steps before I reach the answer:

= -sinx(√3/2) - sinx(√3/2)
= -√3sinx

I'm curious why you don't add the two sinx's together such that the answer would be -√3 2sinx? I'm going to assume that this is a specific reason behind this that applies to all trig functions, but I would appreciate some specific clarification on this case in particular. I know that the distributive law does not apply to sine function, so maybe that relates to my confusion.

4. ## Re: Simpifying trigonometric expression

it's just combining like terms ...

$-\dfrac{\sqrt{3}}{2} \cdot \sin{x} - \dfrac{\sqrt{3}}{2} \cdot \sin{x} = -2\left(\dfrac{\sqrt{3}}{2} \cdot \sin{x}\right) = -\cancel{2}\left(\dfrac{\sqrt{3}}{\cancel{2}} \cdot \sin{x}\right)$

5. ## Re: Simpifying trigonometric expression

Originally Posted by otownsend
Ok I got the right answer after I corrected the formula. Thanks for your help.

I have one last question. And it is regarding the last two steps before I reach the answer:

= -sinx(√3/2) - sinx(√3/2)
= -√3sinx

I'm curious why you don't add the two sinx's together such that the answer would be -√3 2sinx?
You seem to be missing the "/2" part! (√3/2)+ (√3/2)= √3, not 2√3.

I'm going to assume that this is a specific reason behind this that applies to all trig functions, but I would appreciate some specific clarification on this case in particular. I know that the distributive law does not apply to sine function, so maybe that relates to my confusion.

6. ## Re: Simpifying trigonometric expression

Cool. Makes sense. Thank you very much!