How do you simplify $\frac{cot x}{csc x}$ $cotx / (cscx)$ ?

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How do you simplify $\frac{cot x}{csc x}$ $cotx / (cscx)$ ?

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Answer 1 · 2015-12-05T19:38:34

$cos x$ $cosx$

Explanation:

Recall:
$1 . cot x = \frac{1}{tan x}$ $1. cotx=1/tanx$ or $\frac{cos x}{sin x}$ $cosx/sinx$
$2 . csc x = \frac{1}{sin x}$ $2. cscx=1/sinx$

Substitute your reciprocal and quotient identities into the equation:

$\frac{cot x}{csc x}$ $cotx/cscx$

$= \frac{\frac{cos x}{sin x}}{\frac{1}{sin x}} \Leftarrow$ $=(cosx/sinx)/(1/sinx)lArr$ use $cot x = \frac{cos x}{sin x}$ $cotx=cosx/sinx$ instead of $\frac{1}{tan x}$ $1/tanx$

$= \frac{cos x}{sin x} \div \frac{1}{sin x}$ $=cosx/sinx-:1/sinx$

$= \frac{cos x}{sin x} \cdot \frac{sin x}{1}$ $=cosx/sinx*sinx/1$

$=cosx/color(red)cancelcolor(black)sinx*color(red)cancelcolor(black)sinx/1$

$=cosx$

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How do you simplify $\frac{cot x}{csc x}$ $cotx / (cscx)$ ?

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