Question 1209561
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If 7^sin²x - 7^cos²x = 8
find the value of x.
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The starting equation is


            7^(sin^2(x)) - 7^(cos^2(x)) = 8.



Due to  OBVIOUS  reasons,  this equation has no real solutions.


Indeed,  sin^2(x)  has the maximum value of  1;   hence,   7^(sin^2(x))  has maximum value of 7.


Next,  from  7^(sin^2(x)),  the equation subtracts  7^(cos^2(x)),  which is non-negative
real number,  so the left side of the equation  CAN  NOT  be greater than  7.


            A fortiori,  it can not be  8.


At this point,  my solution is complete, and the 


<U>ANSWER</U> &nbsp;&nbsp;is: &nbsp;&nbsp;this given equation has no solution/solutions in real numbers.