What is the limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x)) ?

The limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x)) is 1

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limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x))

x \to \frac{π}{4} lim (\frac{ln ( tan ( x ) )}{1 - cot ( x )})

1

Solution steps

x \to \frac{π}{4} lim (\frac{ln ( tan ( x ) )}{1 - cot ( x )})

Apply L'Hopital's Rule

: x \to \frac{π}{4} lim (\frac{2 csc ( 2 x )}{csc ^{2} ( x )})

= x \to \frac{π}{4} lim (\frac{2 csc ( 2 x )}{csc ^{2} ( x )})

Plug in the value

x = \frac{π}{4}

= \frac{2 csc ( 2 \cdot \frac{π}{4} )}{csc ^{2} ( \frac{π}{4} )}

Simplify

\frac{2 csc ( 2 \cdot \frac{π}{4} )}{csc ^{2} ( \frac{π}{4} )} : 1

= 1

x \to \frac{1}{3} lim (6 x - 1)

x \to 0 lim (x (ln (x) - 1))

x \to 0 lim ((1 + \frac{2}{x})^{3 x})

x \to 8 - lim (2^{x})

x \to \infty lim (\frac{1}{x} - x)

What is the limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x)) ?
The limit as x approaches pi/4 of (ln(tan(x)))/(1-cot(x)) is 1