document.write( "Question 1162366: Solve the following trig equation:
\n" ); document.write( "𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥: 2 sin(𝑥) tan(𝑥) − tan(𝑥) = 1 − 2 sin(𝑥) in the interval [0, 2𝜋] \n" ); document.write( "

Algebra.Com's Answer #786166 by greenestamps(13216) $\"\"$ $\"About$

You can put this solution on YOUR website!

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

\n" ); document.write( "Take a look at the given terms and look for an easier way.

\n" ); document.write( " $\"2sin%28x%29tan%28x%29-tan%28x%29=1-2sin%28x%29\"$

\n" ); document.write( "Factor out the common tan(x) on the left:

\n" ); document.write( " $\"tan%28x%29%282sin%28x%29-1%29+=+1-2sin%28x%29\"$

\n" ); document.write( "Now you might see a quick path to solving the equation -- there is a common factor of 2sin(x)-1:

\n" ); document.write( " $\"tan%28x%29%282sin%28x%29-1%29%2B%282sin%28x%29-1%29+=+0\"$
\n" ); document.write( " $\"%28tan%28x%29%2B1%29%282sin%28x%29-1%29+=+0\"$
\n" ); document.write( " $\"tan%28x%29+=+-1\"$ OR $\"2sin%28x%29+=+1\"$

\n" ); document.write( "Presumably, if you are working on a problem like this, you know how to finish from there....

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