document.write( "Question 358878: solve the equation on the interval (0,2pi)
\n" ); document.write( "tan (x/3) = root 3 \n" ); document.write( "

Algebra.Com's Answer #256179 by robertb(5830) $\"\"$ $\"About$

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$\"tan+%28x%2F3%29+=+sqrt%283%29\"$ ,
\n" ); document.write( " $\"%28tan+%28x%2F3%29%29%5E2+=+3\"$ ,after both sides.
\n" ); document.write( " $\"1%2B%28tan+%28x%2F3%29%29%5E2+=+4\"$ ,
\n" ); document.write( " $\"%28sec+%28x%2F3%29%29%5E2+=+4\"$ , by a Pythagorean identity.
\n" ); document.write( " $\"%28cos%28x%2F3%29%29%5E2+=+1%2F4\"$ , after taking reciprocals.
\n" ); document.write( " $\"cos%28x%2F3%29+=+1%2F2\"$ or $\"cos%28x%2F3%29+=-+1%2F2\"$ .
\n" ); document.write( "The first equation gives $\"x%2F3+=+pi%2F3\"$ , the second $\"x%2F3+=+%284%2Api%29%2F3\"$ .
\n" ); document.write( "further simplification gives $\"x+=+pi\"$ and $\"x+=+4%2Api\"$ . The second answer is not acceptable, therefore the final answer is $\"x+=+pi\"$ .
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