What is the limit as x approaches pi/2 of (tan(x))^{x/2-x} ?

The limit as x approaches pi/2 of (tan(x))^{x/2-x} is Does not exist

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limit as x approaches pi/2 of (tan(x))^{x/2-x}

x \to \frac{π}{2} lim ((tan (x))^{\frac{x}{2} - x})

Does not exist

Solution steps

x \to \frac{π}{2} lim ((tan (x))^{\frac{x}{2} - x})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to \frac{π}{2} + lim ((tan (x))^{\frac{x}{2} - x}) =

Does not exist

x \to \frac{π}{2} - lim ((tan (x))^{\frac{x}{2} - x}) = 0

= Does not exist

What is the limit as x approaches pi/2 of (tan(x))^{x/2-x} ?
The limit as x approaches pi/2 of (tan(x))^{x/2-x} is Does not exist