# Question #aa149

##### 1 Answer

#### Explanation:

First, set the equation equal to zero. Do this by subtracting the

#sinxtan^2x - sinx = 0#

Now, noticing that each term has at least one

#color(blue)(sinx)color(red)((tan^2x - 1)) = 0#

We have made it much easier to solve! Set each factor (whatever is being multiplied) equal to zero and solve.

#color(blue)(sin x) =0# ...and...#color(red)(tan^2x-1) = 0#

Let's being with the equation on the left.

#color(blue)(sin x) = 0#

Think back to the location on the unit circle where

This happens when the radian value is

#color(blue)(x) = 0#

#color(blue)(x) = pi#

We have found two solutions for

#color(red)(tan^2x-1) = 0#

To solve, begin by isolating the

#color(red)(tan^2x) = 1#

Next we have to take the square root of both sides.

#color(red)(sqrt(tan^2x)) = sqrt(1)#

Since the square root of something squared is itself and the square root of **and** positive

#color(red)(tanx) = 1# ...and...#color(red)(tanx) = -1#

At this point, we have to think back again to the unit circle. Since

This is true when the radian value is

**These are all of the solutions we found. Let's review our steps:**

*1.) Get all terms to one side and set the equation equal to zero.*

*2). Factor (doesn't work in every equation, but was useful here).*

*3). Set each factor equal to zero and solve using the unit circle.*