Tan(x)*cos(x)+tan(x)=0?

Question

Solving for x with answers from the unit circle.

Something about identities?

So far I've gotten that tan(x)*cos(x) = sin(x) and then tan(x) = sin(x)/cos(x),but that doesn't really help me.

Answer 1

Factor your equation.  tan(x) will factor out.

tan(x) * (cos(x) + 1) = 0.

Do you know the next step?

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The equation you want to solve is this:

tan(x)*cos(x) + tan(x) = 0

There is a factor of tan(x) in both the terms, so we can factor it out:

tan(x) * (cos(x) + 1) = 0

[Check it: tan(x) * (cos(x) + 1) = tan(x)*cos(x) + tan(x) * 1

which is what we wanted]

Now that we have that the product of two terms equals zero:

tan(x) * (cos(x) + 1) = 0

We can use the so-called "zero-product property" to get

tan(x) = 0 ...... or ...... cos(x) + 1 = 0

We've now split it into two equations that you should be able to solve using your unit circle.