### Home > APCALC > Chapter 1 > Lesson 1.4.4 > Problem1-187

1-187.

Solve the following equations for all values of x in the domain [0, 2π). Use exact values. Homework Help ✎

1. sin(2x) = sin(x)

sin(2x) = 2sin(x)cos(x). Substitute and solve for x.

There will be four solutions.

2. sin(x + π) + cos$( x - \frac { \pi } { 2 } )$ = 1

$\text{sin}(x+\pi)+\text{cos}\left(x-\frac{\pi}{2}\right)=-\text{sin}(x)+\text{cos}(x)\text{cos}\left(\frac{\pi}{2}\right)+\text{sin}(x)\text{sin}\left(\frac{\pi}{2}\right)$

There is no solution to this problem.

3. cot(x) – tan(x) = 2$\sqrt { 3 }$

$\text{cot}(x)=\frac{\text{cos}(x)}{\text{sin}(x)}\ \ \ \ \ \text{tan}(x)=\frac{\text{sin}(x)}{\text{cos}(x)}$

There will be four solutions.