What is the limit as x approaches pi/2 of (1-tan(2x))/(2tan(x)) ?

The limit as x approaches pi/2 of (1-tan(2x))/(2tan(x)) is 0

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limit as x approaches pi/2 of (1-tan(2x))/(2tan(x))

x \to \frac{π}{2} lim (\frac{1 - tan ( 2 x )}{2 tan ( x )})

0

Solution steps

x \to \frac{π}{2} lim (\frac{1 - tan ( 2 x )}{2 tan ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot x \to \frac{π}{2} lim (\frac{1 - tan ( 2 x )}{tan ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{1}{2} \cdot \frac{lim _{x \to \frac{π}{2}} ( 1 - tan ( 2 x ) )}{lim _{x \to \frac{π}{2}} ( tan ( x ) )}

x \to \frac{π}{2} lim (1 - tan (2 x)) = 1

x \to \frac{π}{2} lim (tan (x)) = - \infty

= \frac{1}{2} \cdot \frac{1}{- \infty}

Simplify

\frac{1}{2} \cdot \frac{1}{- \infty} : 0

= 0

What is the limit as x approaches pi/2 of (1-tan(2x))/(2tan(x)) ?
The limit as x approaches pi/2 of (1-tan(2x))/(2tan(x)) is 0