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document.write( "if 2costheta=x=1/x, 2cosphi=y+1/y,2coslamida=z+1/z,then prove that 2cos(theta+phi+lamida)=xyz+1/(xyz).
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document.write( "plz send me ans as early as possible.
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document.write( "Obviously, the post contains the error (the typo ?) in this part \"2costheta = x=1/x\", which must be read as \"2costheta = x+(1/x)\".\r
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document.write( "With this editing, the solution is as follows.\r
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document.write( "1. If 2*cos(theta) = x + (1/x), it implies that \r\n" );
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document.write( " EITHER x = 1 and then 2cos(theta) = 1 + (1/1) = 2 ====> cos(theta) = 1 ====> theta = 0,\r\n" );
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document.write( " OR x = -1 and then 2cos(theta) = -1 + (1/(-1)) = -2 ====> cos(theta) = -1 ====> theta = 
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document.write( " It is simply because x + (1/x) >= 2 if x is positive, or\r\n" );
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document.write( " x + (1/x) <= -2 if x is negative,\r\n" );
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document.write( " which is VERY WELL KNOWN fact.\r\n" );
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document.write( "2. Similarly, from the given data \r\n" );
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document.write( " cos(phi) = +/-1 and phi = 0 or phi = .\r\n" );
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document.write( " cos(lambda) = +/-1 and lambda = 0 or lambda = .\r\n" );
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document.write( "3. Now, if theta=0, phi=0 and lambda=0\r\n" );
document.write( " (equivalently, all three cosines are equal to 1)\r\n" );
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document.write( " then 2cos(theta+phi+lamida)=xyz+1/(xyz) is, obviously, true.\r\n" );
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document.write( " Also, if theta=, phi= and lambda=\r\n" );
document.write( " (equivalently, all three cosines are equal to -1)\r\n" );
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document.write( " then 2cos(theta+phi+lamida)=xyz+1/(xyz) is, obviously, true, again.\r\n" );
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document.write( " Finally, if any other combination of possible angles is chosen, \r\n" );
document.write( " it will lead to the same equality, as it is easy to check, having very restricted number of combinations.\r\n" );
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document.write( "SOLVED.\r
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document.write( "The key idea of the solution above is this fact:\r\n" );
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document.write( " if x is the positive real number, then 
>=2, \r\n" );
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document.write( " and the equality takes place if and only if x = 1.\r\n" );
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document.write( "Proof\r\n" );
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document.write( " = 
is greater than or equal to 2.\r\n" );
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document.write( "The equality takes place if and only if 
= 0, which is equivalent to \r\n" );
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document.write( "
= 0 <=== equivalent to ===> 
= 
<=== equivalent to ===> x = 1 (under the assumption that x is positive).\r\n" );
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document.write( "The proof is completed.\r\n" );
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document.write( " Notice. If you have questions or need more help, you can send a message to me through the \"Thank you\" form note.\r\n" );
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document.write( " In this case PLEASE do not forget to refer to the problem ID number, which is 1095761, \r\n" );
document.write( " in order for I could identify the problem.\r\n" );
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