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

The limit as x approaches pi/2 of (sin(x)-cos(x))^{tan(x)} is 1/e

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

x \to \frac{π}{2} lim ((sin (x) - cos (x))^{t a n (x)})

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

x \to \frac{π}{2} lim ((sin (x) - cos (x))^{t a n (x)})

Apply exponent rules

= x \to \frac{π}{2} lim (e^{t a n (x) l n (s i n (x) - c o s (x))})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

What is the limit as x approaches pi/2 of (sin(x)-cos(x))^{tan(x)} ?
The limit as x approaches pi/2 of (sin(x)-cos(x))^{tan(x)} is 1/e