What is the limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))} ?

The limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))} is 1

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limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))}

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}})

1

Solution steps

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i 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 ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}}) = 1

x \to 0 + lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}}) = 1

= 1

What is the limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))} ?
The limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))} is 1