document.write( "Question 979124: if 0≤Θ<360°, solve sec^2 (2Θ) +2sec(2Θ) = 0 \n" ); document.write( "

Algebra.Com's Answer #600448 by KMST(5328) $\"\"$ $\"About$

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If $\"0%5Eo%3C=theta%3C360%5Eo\"$ <--> $\"0%5Eo%3C=2theta%3C720%5Eo\"$ , solve $\"sec%5E2%282theta%29%2B2sec%282theta%29=0\"$
\n" ); document.write( "Factoring:
\n" ); document.write( " $\"sec%5E2%282theta%29%2B2sec%282theta%29=0\"$ ---> $\"sec%282theta%29%28sec%282theta%29%2B2%29=0\"$ ---> $\"system%28sec%282theta%29=0%2C%22or%22%2Csec%282theta%29%2B2=0%29\"$
\n" ); document.write( " $\"sec%282theta%29=0\"$ does not happen for any value of $\"theta\"$ ,
\n" ); document.write( "because the function secant never takes any value between -1 and 1.
\n" ); document.write( " $\"sec%282theta%29%2B2=0\"$ --> $\"sec%282theta%29=-2\"$ --> $\"1%2Fcos%282theta%29=-2\"$ --> $\"cos%282theta%29=-1%2F2\"$ --> $\"2theta=k%2A360%5Eo+%2B-+120%5Eo\"$ for some integer $\"k\"$ .
\n" ); document.write( "With the restriction $\"0%5Eo%3C=2theta%3C720%5Eo\"$ ,
\n" ); document.write( "the values that make $\"2theta=k%2A360%5Eo+%2B-+120%5Eo\"$ for some integer $\"k\"$ are
\n" ); document.write( " $\"2theta=120%5Eo\"$ <---> $\"highlight%28theta=60%5Eo%29\"$ , or
\n" ); document.write( " $\"2theta=240%5Eo\"$ <---> $\"highlight%28theta=120%5Eo%29\"$ , or
\n" ); document.write( " $\"2theta=480%5Eo\"$ <---> $\"highlight%28theta=240%5Eo%29\"$ , or
\n" ); document.write( " $\"2theta=600%5Eo\"$ <---> $\"highlight%28theta=300%5Eo%29\"$ . \n" ); document.write( "

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