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]

Algebra ->  Trigonometry-basics -> 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]      Log On


   

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(13215) About Me  (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.

2sin%28x%29tan%28x%29-tan%28x%29=1-2sin%28x%29

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

tan%28x%29%282sin%28x%29-1%29+=+1-2sin%28x%29

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

tan%28x%29%282sin%28x%29-1%29%2B%282sin%28x%29-1%29+=+0
%28tan%28x%29%2B1%29%282sin%28x%29-1%29+=+0
tan%28x%29+=+-1 OR 2sin%28x%29+=+1

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