document.write( "Question 1209561: If 7^sin²x - 7^cos²x = 8
\n" ); document.write( "find the value of x.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #849523 by ikleyn(53763)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "If 7^sin²x - 7^cos²x = 8
\n" ); document.write( "find the value of x.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The starting equation is\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "         7^(sin^2(x)) - 7^(cos^2(x)) = 8.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Due to  OBVIOUS  reasons,  this equation has no real solutions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Indeed,  sin^2(x)  has the maximum value of  1;  hence,  7^(sin^2(x))  has maximum value of 7.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Next,  from  7^(sin^2(x)),  the equation subtracts  7^(cos^2(x)),  which is non-negative
\n" ); document.write( "real number,  so the left side of the equation  CAN  NOT  be greater than  7.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "         A fortiori,  it can not be  8.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "At this point,  my solution is complete, and the \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "ANSWER   is:   this given equation has no solution/solutions in real numbers.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );