document.write( "Question 1206408: Please help me with this equation.
\n" ); document.write( "An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
\n" ); document.write( "1 − 2 sin(𝜃) = cos(2𝜃)
\n" ); document.write( "Find the solutions in the interval [0, 2𝜋). \n" ); document.write( "
Algebra.Com's Answer #843857 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "An equation is given. (Enter your answers as a comma-separated list. Let k be any integer.
\n" ); document.write( "Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
\n" ); document.write( "1 − 2 sin(𝜃) = cos(2𝜃)
\n" ); document.write( "Find the solutions in the interval [0, 2𝜋).
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @MathLover1 is  INCORRECT.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "\"1+-2+sin%28theta%29+=+cos%282theta%29\"\r\n" );
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document.write( "Find the solutions in the interval [\"0\", \"2pi\").\r\n" );
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document.write( "\"1+-2+sin%28theta%29+=+cos%282theta%29\"....use identity \"cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29\"\r\n" );
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document.write( "\"1+-2+sin%28theta%29+=+cos%5E2%28theta%29+-+sin%5E2%28theta%29\"\r\n" );
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document.write( "\"sin%5E2%28theta%29-cos%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0\"...use identity \"cos%5E2%28theta%29=1-sin%5E2%28theta%29\"\r\n" );
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document.write( "\"sin%5E2%28theta%29-%281-sin%5E2%28theta%29%29+-2+sin%28theta%29+%2B1=+0\"\r\n" );
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document.write( "\"sin%5E2%28theta%29-1%2Bsin%5E2%28theta%29+-2+sin%28theta%29+%2B1=+0\"\r\n" );
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document.write( "\"2sin%5E2%28theta%29+-2+sin%28theta%29+=+0\"...factor\r\n" );
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document.write( "\"2sin%28theta%29%28sin%28theta%29+-1%29++=+0\"\r\n" );
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document.write( "If  \"sin%28theta%29+=+0\"  then  \"theta\" = 0  or  \"theta\" = \"pi\" radians.\r\n" );
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document.write( "If  \"sin%28theta%29+=+1\"  then  \"theta\" = \"pi%2F2\".\r\n" );
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document.write( "ANSWER.  In the given interval, there are three and only three solutions, \r\n" );
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document.write( "         x = 0,   x = \"pi%2F2\" = 1.571 radians  and   x = \"pi\" = 3.142 radians (rounded as requested).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (correctly)\r
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\n" ); document.write( "\n" ); document.write( "The post is written INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "If you need the solution in the interval [0,\"2pi\"),
\n" ); document.write( "then you do not need to mention about \"an arbitrary integer k\".\r
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