What is the limit as x approaches 0 of (sin(x))/(-2tan(x)sec^2(x)) ?

The limit as x approaches 0 of (sin(x))/(-2tan(x)sec^2(x)) is -1/2

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limit as x approaches 0 of (sin(x))/(-2tan(x)sec^2(x))

x \to 0 lim (\frac{sin ( x )}{- 2 tan ( x ) sec ^{2} ( x )})

- \frac{1}{2}

Decimal

- 0.5

Solution steps

x \to 0 lim (\frac{sin ( x )}{- 2 tan ( x ) sec ^{2} ( x )})

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

= \frac{1}{- 2} \cdot x \to 0 lim (\frac{sin ( x )}{tan ( x ) sec ^{2} ( x )})

Simplify

= (- \frac{1}{2}) \cdot x \to 0 lim (\frac{sin ( x )}{tan ( x ) sec ^{2} ( x )})

Express with sin, cos

= (- \frac{1}{2}) \cdot x \to 0 lim (cos^{3} (x))

Plug in the value

x = 0

= (- \frac{1}{2}) cos^{3} (0)

Simplify

(- \frac{1}{2}) cos^{3} (0) : - \frac{1}{2}

= - \frac{1}{2}

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