document.write( "Question 384531: The solutions of cos2x – cos x – 2 = 0 are (where k denotes an arbitrary integer)\r
\n" ); document.write( "\n" ); document.write( "I know the answer is −π + 2kπ, I just have no idea how to get to that point. \n" ); document.write( "

Algebra.Com's Answer #272497 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
If you let z = cos x, then the equation becomes a simple quadratic:\r
\n" ); document.write( "\n" ); document.write( " $\"z%5E2+-+z+-+2+=+0\"$ (I hope the cos2x means $\"cos%5E2+%28x%29\"$ , otherwise we'd need the power reduction formulas).\r
\n" ); document.write( "\n" ); document.write( "From the quadratic, we can factor and obtain $\"%28z+-+2%29%28z+%2B+1%29+=+0\"$ --> z = 2 or z = -1. However, z is only defined on [-1, 1] since it is the range of cosine, so z = -1, and x = -pi (plus any multiple of 2pi since they denote the same angle on a unit circle).\r
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