Sin theta= sin theta tan theta

[Coco12]

Problem statement
Solve each equation over the domain theta greater than or equal to 0, less than or equal to 2 pi:

Sin theta= sin theta tan theta

Revelant equations

Problem statement

I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third quadrant. So from there I solve accordingly. Is this right?

 

[Chestermiller]

Problem statement
Solve each equation over the domain theta greater than or equal to 0, less than or equal to 2 pi:

Sin theta= sin theta tan theta

Revelant equations

Problem statement

I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third quadrant. So from there I solve accordingly. Is this right?

What about the sinθ?

 

[Mark44]

I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third quadrant. So from there I solve accordingly. Is this right?

No.
When you divide both sides by sinθ, you lose solutions. Instead, rewrite the equation like so -
sinθ - sinθ tanθ = 0
and then factor the left side.

 

[Coco12]

No.
When you divide both sides by sinθ, you lose solutions. Instead, rewrite the equation like so -
sinθ - sinθ tanθ = 0
and then factor the left side.

Oh... I see it now.