What is the limit as x approaches 0 of (1-cos(x))^{tan(x)} ?

The limit as x approaches 0 of (1-cos(x))^{tan(x)} is 1

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limit as x approaches 0 of (1-cos(x))^{tan(x)}

x \to 0 lim ((1 - cos (x))^{t a n (x)})

1

Solution steps

x \to 0 lim ((1 - cos (x))^{t a n (x)})

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

then

x \to a lim f (x) = L

x \to 0 - lim ((1 - cos (x))^{t a n (x)}) = 1

x \to 0 + lim ((1 - cos (x))^{t a n (x)}) = 1

= 1

What is the limit as x approaches 0 of (1-cos(x))^{tan(x)} ?
The limit as x approaches 0 of (1-cos(x))^{tan(x)} is 1