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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to - 1 lim (7)

x \to - 3 lim (\frac{x ^{2} - 2}{x - 4})

x \to - 2 lim (3 x - 4 x^{2})

x \to 0 lim ((x^{2})^{x^{2}})

x \to 6 - lim (\frac{2 x}{x ^{2} - 36})

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