SOLUTION: Solve the following trig equation: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥: 2 sin(𝑥) tan(𝑥) − tan(𝑥) = 1 − 2 sin(𝑥) in the interval [0, 2𝜋]

Question 1162366: Solve the following trig equation:
𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥: 2 sin(𝑥) tan(𝑥) − tan(𝑥) = 1 − 2 sin(𝑥) in the interval [0, 2𝜋]
Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

Your first impulse might be to change each tan(x) to sin(x)/cos(x). But that path will make the work much harder.

Take a look at the given terms and look for an easier way.

Factor out the common tan(x) on the left:

Now you might see a quick path to solving the equation -- there is a common factor of 2sin(x)-1:

OR

Presumably, if you are working on a problem like this, you know how to finish from there....

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